Physics

Educational objectives

GENERAL OBJECTIVES:
Aim of the course is to introduce the basic notions of the modern theory of gravity, and of its more important conceptual and astrophysical implications.

At the end of the course the student should: 1) have acquired the instruments of differential geometry which allow to formulate Einstein's equations and derive its predictions. 2) Have understood what is the role of the equivalence principle between gravitational and inertial mass in the formulation of the theory, and why the gravitational field modifies the spacetime geometry. 3) Have understood how to use the symmetries of a physical problem to simplify Einstein's equations and find solutions. 4) Be able to derive the solution describing the gravitational field external to a
non rotating, spherically symmetric body (the Schwarzschild solution), and to show that this solution can also represent a non rotating black hole. 5) Have understood how some of the main predictions of General Relativity can be obtained by solving the geodesic equations, which describe the motion of free particles in a gravitational field. 6) Have understood how to solve Einstein's equations in the weak field limit, to show that spacetime perturbations propagate as gravitational
waves.

Therefore, at the end of the course the student should: 1) be able to compute how vectors, one-forms and tensors transform under a coordinate transformation; to compute the covariant derivative of these geometrical objects and to solve exercises which involve these operations in tensor equations. 2) Be able to compute how does a vector change when parallely transported along a path in curved spacetime, and to derive the curvature tensor using this operation. 3) Be able to derive Einstein's equations. 4) Be able to derive and interpret some of the most interesting predictions of General Relativity: the gravitational redshift, light deflection near massive bodies, precession of Mercury perihelion, existence of gravitational waves.

This course introduces the fundamental concept of a curved spacetime due to the existence of a gravitational field, and discusses the more important aspects of the scientific revolution introduced by Einstein's theory. As such, it is a basic course for the laurea magistrale in Astronomy and Astrophysics, and it is also a matter which should be part of the cultural background of a modern physicist.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) Know the basics of differential geometry
OF 2) Know the basics of General Relativity and its most relevant concepts, including that of a black hole and gravitational waves
OF 3) Know and interpret the observational applications of the theo
B - Application skills
OF 4) Be able to perform analytical calculations of differential geometry
OF 5) Knowing how to derive Einstein's equations for the gravitational field
OF 6) Knowing how to derive and interpret some of the most important effects predicted by General Relativity
OF 7) Knowing how to calculate the geodetic motion in the spacetime of a black hole
C - Autonomy of judgment
OF 8) To fully understand the concept of curved spacetime, change of coordinates, and the consequences of the principles of Equivalence and General Covariance
D - Communication skills
OF 9) Knowing how to present in written and oral form the main derivations concerning formulas and theorems of differential geometry
OF 10) Knowing how to present in written and oral form the main derivations concerning General Relativity: Einstein equations, geodesic motion, metrics of a black hole, gravitational waves
E - Ability to learn
OF 11) Have the ability to apply the knowledge of the course to understand and derive more advanced topics

Educational objectives

The aim of the course is to learn the experimental evidences and the
methodologies that led to the formulation of the Standard Model (SM) of
elementary particle physics, from the beginning of the discipline in the
30s and 40s of the last century until the formulation of the SM. The
course is closely linked to the theoretical courses of the first
semester and to the annual course of Laboratory.

At the end of the course the students have to:
1) know and be able to discuss the fundamental concepts of the SM
2) know the fundamental experiments that allowed the development of the SM
3) to have understood the main methodologies of the experimental
particle physics, both the technological and the statistical aspects.

Educational objectives

GENERAL OBJECTIVES:

This course will introduce the student to the most important concepts, ideas and tools of quantum field theory which has become the universal framework to describe all fundamental forces in nature. The student will understand how to construct field theories, quantize them in the presence of interactions and how to apply advanced techniques of regularization and renormalisation. The course will include the mathematical structure of non-Abelian gauge theories and their role in our present understanding of fundamental forces of Nature.

SPECIFIC OBJECTIVES:

A - Knowledge and understanding

The goal is for students to develop a critical understanding of the topics covered during the course, both as regards the purely theoretical aspects and in relation to the applications to different physical phenomena, and that they develop an adequate knowledge of the methods applied in theoretical physics, with particular reference to the methods usually used to conduct research in this sector.

B - Application skills

Alongside understanding the topics and methods used during the lessons, one of the objectives of the course is to enable students to apply those same methods to new problems, be they study or research.

C - Autonomy of judgment

One of the main objectives of the course is for students to develop critical skills with respect to the topics covered. They are often encouraged to follow other paths (than those followed during the lectures) for the achievement of results, or to propose interpretations or readings different from those presented by the teacher of the same results. Often during the lessons students are asked to make suggestions or make estimates in relation to specific calculations, with the aim of encouraging their autonomy of thought and their ability to make choices when confronted with delicate steps.

D - Communication skills

The course aims to increase students' communication skills, providing them with methodological tools that allow them to improve their ability to discuss in an original way topics related to theoretical and applicative aspects of quantum field theory.

E - Ability to learn

One of the most important objectives of the course is to provide students with a methodology that allows them to have access to a continuous updating of knowledge, trying in particular to increase their ability to deal with specialized literature.

Educational objectives

GENERAL OBJECTIVES:
Aim of the course is to introduce the basic notions of the modern theory of gravity, and of its more important conceptual and astrophysical implications.

At the end of the course the student should: 1) have acquired the instruments of differential geometry which allow to formulate Einstein's equations and derive its predictions. 2) Have understood what is the role of the equivalence principle between gravitational and inertial mass in the formulation of the theory, and why the gravitational field modifies the spacetime geometry. 3) Have understood how to use the symmetries of a physical problem to simplify Einstein's equations and find solutions. 4) Be able to derive the solution describing the gravitational field external to a
non rotating, spherically symmetric body (the Schwarzschild solution), and to show that this solution can also represent a non rotating black hole. 5) Have understood how some of the main predictions of General Relativity can be obtained by solving the geodesic equations, which describe the motion of free particles in a gravitational field. 6) Have understood how to solve Einstein's equations in the weak field limit, to show that spacetime perturbations propagate as gravitational
waves.

Therefore, at the end of the course the student should: 1) be able to compute how vectors, one-forms and tensors transform under a coordinate transformation; to compute the covariant derivative of these geometrical objects and to solve exercises which involve these operations in tensor equations. 2) Be able to compute how does a vector change when parallely transported along a path in curved spacetime, and to derive the curvature tensor using this operation. 3) Be able to derive Einstein's equations. 4) Be able to derive and interpret some of the most interesting predictions of General Relativity: the gravitational redshift, light deflection near massive bodies, precession of Mercury perihelion, existence of gravitational waves.

This course introduces the fundamental concept of a curved spacetime due to the existence of a gravitational field, and discusses the more important aspects of the scientific revolution introduced by Einstein's theory. As such, it is a basic course for the laurea magistrale in Astronomy and Astrophysics, and it is also a matter which should be part of the cultural background of a modern physicist.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) Know the basics of differential geometry
OF 2) Know the basics of General Relativity and its most relevant concepts, including that of a black hole and gravitational waves
OF 3) Know and interpret the observational applications of the theo
B - Application skills
OF 4) Be able to perform analytical calculations of differential geometry
OF 5) Knowing how to derive Einstein's equations for the gravitational field
OF 6) Knowing how to derive and interpret some of the most important effects predicted by General Relativity
OF 7) Knowing how to calculate the geodetic motion in the spacetime of a black hole
C - Autonomy of judgment
OF 8) To fully understand the concept of curved spacetime, change of coordinates, and the consequences of the principles of Equivalence and General Covariance
D - Communication skills
OF 9) Knowing how to present in written and oral form the main derivations concerning formulas and theorems of differential geometry
OF 10) Knowing how to present in written and oral form the main derivations concerning General Relativity: Einstein equations, geodesic motion, metrics of a black hole, gravitational waves
E - Ability to learn
OF 11) Have the ability to apply the knowledge of the course to understand and derive more advanced topics

Educational objectives

GENERAL OBJECTIVES:

The main goal of the course is to introduce students to the mathematical theory of groups (mainly: discrete groups and compact Lie groups) by a Mathematical Physics approach which emphasizes the role of representations of symmetries in terms of states or observables of the corresponding theory. Such an approach allows an immediate comparison between classical theories (Poisson brackets) and quantum theories (commutators).

SPECIFIC OBJECTIVES:

A - Knowledge and understanding
OF1) To know the fundamental concepts in the theory of finite groups and matrix Lie groups, and in the theory of their linear, unitary or projective representations.
OF2) To know the mathematical structure of the Lie groups which more often appear in physical theories, and to understand the relation between such groups and the symmetries of the physical theory.
OF3) To understand the role of symmetries and Lie groups in (relativistic) field theories.
OF4) To understand the mathematical language of differential forms, and the reformulation of electromagnetism in such a language.

B – Application skills
OF 5) To be able to compute the commutation relations among the generators of the Lie algebra of a given (matrix) Lie group; to be able to explicitly compute such commutation relations in the most relevant cases: the rotation group, the Poincaré group, and the group SU(3).
OF 6) To be able to compute the tensor product of two representations of the rotation group, by using the Wigner Eckart theorem; to be able to interpret the result of such a computation in the application to compound systems (e.g. molecules).
OF7) To be able to determine whether a given differential form is closed and/or exact; to be able to translate the concepts concerning differential forms in the analogous concepts of vector analysis (gradient, curl or rotational, divergence) and vice versa.

C - Autonomy of judgment
OF 8) To be able to critically read an advanced book on symmetries in physics.
OF 9) To be able to integrate the knowledge acquired within the course, in order to apply them in the context of different physical theories, in connection e.g. with high energy physics or with condensed matter physics.

D – Communication skills
OF 10) Ability to discuss the symmetries of a physical system by appropriately using the language of differential forms and Lie groups.

E - Ability to learn
OF 11) Ability to read advanced monographies and research papers, which usually use the mathematical language of Lie groups and differential forms.
OF 12) Ability to "construct" a physical theory, by implementing in the theory the symmetries of the physical system under investigation, using Lie algebras and Lie groups as a fundamental tool.

Educational objectives

Aim of the Course is to provide the basic knowledge of Nuclear Physics at the present stage, recalling the strong interplay with other fields of Physics , both at the frontier of the research in the subnuclear Physics (e.g., stellar evolution, search of signals of new Physics) and on the side of applications , like in medical, environmental and cultural-heritage fields. As a part of the final examination, besides the oral one, students will be asked to give a short presentation, at most 20 slides, of a topic chosen among the ones proposed and according to their interests in the field.

Educational objectives

A - Knowledge and understanding
OF 1) Starting from the study of neurobiology of the nervous system, the student will first concentrate on the mechanisms regulating the electro-chemical properties of nerve cells and their connections, eventually studing the dynamics of populations of neuronal networks. The knowledge acquired will be on nonlinear and statistical physics compared to experimental data.
OF 2) The students will develop generally applicable skills in the field of theoretical physics of the complex systems and the nonlinear dynamics.
B - Application skills
OF 3) The student will be able to understand the dynamics of neuronal populations at the basis of the cognitive functions like decision making and short-term memory.
OF 4) The student will be able to apply analysis techniques and methods to electrophysiological data.
C - Autonomy of judgment
OF 5) By attending the lessons and with the regular interaction during the lessons themselves, the student will develop adequate autonomy of judgment, as he/she will be able to interface constantly with the teacher and critically analyze the information learned.
D - Communication skills
OF 6) The skills on the neurobiology of the nervous system will allow the student to interact with environments different from physics, enabling him/her to initiate multidisciplinary interactions in the life sciences.
E - Ability to learn
OF 7) The student will have the ability to evaluate and solve various problems of both data analysis and physics of complex systems.
OF 8) The acquired knowledge will allow the student to tackle the study of interdisciplinary papers on the physical phenomena underlying the behavior of the nervous system.

Educational objectives

GENERAL OBJECTIVES:
Acquire familiarity with advanced deep learning techniques based on differentiable neural network models with supervised, unsupervised and reinforced learning paradigms; acquire skills in modelling complex problems through deep learning techniques, and be able to apply them to different application contexts in the fields of physics and basic and applied scientific research.

Discussed topics include: general machine learning concepts, differentiable neural networks, regularization techniques. Convolutional neural network, neural network for sequence analysis (RNN, LSTM / GRU, Transformers). Advanced learning techniques: transfer learning, domain adaptation, adversarial learning, self-supervised and contrastive learning, model distillation.
Graph Neural Networks (static and dynamic) and application to structured models for physics: dynamic models, simulation of complex fluids, GNN Hamiltonians and Lagrangians. Generative and variational models: variational mean-field theory, expectation maximization, energy based and maximum entropy models (Hopfield networks, Boltzman machines and RBM), AutoEncoders, Variational AutoEncoders, GANs, Autoregressive flow models, invertible networks, generative models based on GNN. Quantum Neural Networks.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) Knowledge of the functioning of neural networks and their mathematical interpretation as universal approximators
OF 2) Understanding of the limits and potential of advanced machine learning models
OF 3) Understanding of the limits and potential of DL in solving physics problems

B - Application skills
OF 4) Design, implementation, commissioning and analysis of deep learning architectures to solve complex problems in physics and scientific research.

C - Autonomy of judgment
OF 5) To be able to evaluate the performance of different architectures, and to evaluate the generalization capacity of the same

D - Communication skills
OF 6) Being able to clearly communicate the formulation of an advanced learning problem and its implementation, its applicability in realistic contexts
OF 7) Being able to motivate and to evaluate the generalization capacity of a DL model

E - Ability to learn
OF 8) Being able to learn alternative and more complex techniques
OF 9) Being able to implement existing techniques in an efficient, robust and reliable manner

Educational objectives

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) To know the elements of the computer hardware and software architecture and to understand their interactions.
OF 2) To know the techniques needed to develop optimized code for a given computer architecture.
OF 3) To know the fundamentals of logic design of digital circuits using hardware description languages (VHDL).

B - Application skills
OF 4) To be able to evaluate the execution performance of code on a given computer architecture.
OF 5) To be able to develop scientific code optimized for a given computer architecture.
OF 6) To be able to select the computer architecture best suited for a given application.
OF 7) To be able to implement a circuit through VHDL coding and to simulate its behaviour.
C - Autonomy of judgment
OF 8) To be able to integrate the knowledge acquired in order to apply them for the processing needs in the experimental or theoretical Physics.

D - Communication skills

E - Ability to learn
OF 9) Have the ability to follow up the development in computer architectures.

Educational objectives

GENERAL OBJECTIVES:
The course will cover the physics of particle detectors and particle accelerators. It will introduce the experimental techniques used in nuclear, particle physics and photon science, and describe the layout and functionality of modern experiments. History, operating principles of modern particle accelerators and applications in nuclear, sub-nuclear and medical physics will be treated as well.

Through classroom lectures, dedicated seminars held by experts and hands-on exercise sessions, the Detectors and Accelerators in Particle Physics course proposes:
- to deepen the knowledge of the interactions of elementary particles with matter;
- to analyze the functioning of the various detectors used for the detection of elementary particles in nuclear and subnuclear physics;
- to examine some current experiments of greater interest;
- to provide an introduction to the physics of particle accelerators by also presenting future projects;
- to teach how to design and simulate simple experimental using the Geant4 software library.

At the end of the course, students will be familiar with modern detection and particle acceleration methods in particle and applied physics. They will have the basis to understand the motivations and the functioning of the various parts of an experiment in high energy physics or instrumentation for the control of the beams in medical physics laboratories. This will include the ability to size and select detectors suitable for the purposes of the experiments to be examined or to be designed.
They will know how to describe measurements of ionization, position, energy, and momentum of particles, as well as particle identification and timing measurements. They will develop competence in quickly and critically acquiring information from publications other then textbooks.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) To know the fundamentals of particle detectors
OF 2) To know the fundamentals of particle accelerators
OF 3) To understand the language of the physics of particle detectors and accelerators

B - Application skills
OF 4) Ability to design, dimension and choose suitable detectors for a specific particle physics experiment
OF 5) Ability to implement a simple simulation setup with Geant4 for a particle detector
C - Autonomy of judgment
OF 6) To be able to analyze and evaluate the performance of a particle physics detectors
OF 7) To be able to analyze and evaluate the performance of a particle accelerator
D - Communication skills
OF 8) Being able to clearly communicate the operation and properties of a particle detector and of a particle accelerator, and their applicability in realistic contexts
OF 9) Being able to motivate the architectural choices behind a specific particle detector or accelerator design

E - Ability to learn
OF 8) Being able to learn alternative and more complex techniques
OF 9) Being able to implement existing techniques in an efficient, robust and reliable manner

Educational objectives

General Objectives:
To acquire knowledge of fundamental topics in Mathematical Physics and the related mathematical methods.

Specific Objectives:

Knowledge and Understanding:

By the end of the course, students will be familiar with the fundamentals of operator theory in Hilbert spaces, the mathematical structure of quantum mechanics, and the basic methods for studying problems in quantum mechanics from the perspective of mathematical physics.

Applying knowledge and understanding:

Students who pass the exam will be able to: i) apply the results of operator theory, ii) construct self-adjoint Hamiltonians and study their spectra, iii) rigorously approach a scattering problem, iv) understand the mathematical methods required for the study of the dynamics of many-body systems, with particular regard to the phenomenon of condensation.

Critical Thinking and Judgment:

Students who pass the exam will be able to recognize a mathematical-physical approach and analyze similarities and differences compared to the typical approach in Theoretical Physics.

Communication Skills:

Students who pass the exam will have developed the ability to communicate concepts, ideas, and methodologies in mathematical physics.

Learning Skills:

The knowledge acquired will enable students to pursue further study—either independently or through other courses—on more specialized aspects of the methods of mathematical physics.

Educational objectives

GENERAL OBJECTIVES:
Aim of the course is to deepen the knowledge of theoretical aspects of the theory of gravity and of its most important applications in astrophysics: phenomenology of gravitational wave sources, neutron
stars and black hole structure and properties.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) To know the quadrupole formalism and to understand how gravitational radiation reaction affects the evolution of a compact binary system and of a rotating compact star
OF 2) To understand which quantities can be measured using the detection of gravitational waves
OF 3) To know the final stages of stellar evolution as a function of the mass, which is the structure of a whith dwarf and how can it be determined. To understand the concept of critical mass.
OF 4) To know how the equations of Thermodynamics have to be modified in General Relativity.
OF 5) To know how the structure of a neutron star can be determined using the theory of General Relativity
OF 6) To understand the complex phenomenology associated to the motion of bodies and light around a rotating black hole, and some of the astrophysical phenomena involved in these processes.
OF 7) To know how the Einstein equations can be derived using a variational approach.
OF 8) To know how to derive the geodesic equations for a Kerr black hole, discuss their properties in the equatorial plane, both for massive and massless particles.
OF 9) To understand the process of extraction of energy by a rotating black hole
(Penrose's process).

B - Application skills
OF 10) To be able to apply the quadrupole formalism to determine the gravitational waveforms emitted by source in the regime of weak field and slow motion. In particular, to be able to compute the gravitational waveforms emitted by binary systems formed by black holes and neutron stars, and by rotating neutron stars.
OF 11) To be able to compute, for assigned equations of state of nuclear matter, the inner structure of a neutron star, by integrating Einstein's equations, finding the mass and radius of the star.
OF 12) To be able to discuss the mass-radius or mass-central density diagrams for a star, identifying the instability regions.
…
C - Autonomy of judgment
OF 13) To be able to integrate the knowledge acquired in advanced Theoretical Physics courses, such as Quantum Gravity, Alternative Theories of Gravity, String Theory
OF 14) To be able to integrate the knowledge acquired in advanced Relativistic Astrophysics courses

D - Communication skills

E - Ability to learn
OF 15) Have the ability to read scientific papers in order to further explore some of the topics introduced during the course.

Educational objectives

GENERAL OBJECTIVES:
The course aims to provide an overview as complete as possible on the most recent and important results in the field of theoretical and experimental cosmology. In particular, the three main observational evidences for the Big Bang scenario will be discussed: the recession of the galaxies, the primordial nucleosynthesis and the cosmic background radiation. A significant part of the program will be devoted to the study of the anisotropies of cosmic background radiation.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) Ability to derive Friedmann equations starting from General Relativity and FRW metric.
OF 2) To understand the observational methods that have allowed a verification of the current cosmological model.
OF 3) To identify current model issues and discuss possible future developments.
B - Application skills
OF 4) To know how to determine the value of some cosmological parameters starting from different cosmological observables.
C - Autonomy of judgment
OF 5) Being able to understand what are the fundamental characteristics that a cosmological theory must possess in order to have a good agreement with current observations.
E - Ability to learn
OF 6) Have the ability to read scientific papers in order to further explore some of the topics introduced during the course.

Educational objectives

GENERAL OBJECTIVES:
The course is an introduction to the SU(3) symmetry in the construction of the quark model and in quantum chromodynamics (QCD). The second part is devoted to the study of collider physics, from deep inelastic processes to the LHC. The third part is more specifically on QCD. Despite the complexity of the topics covered, the student is expected to master a number of basic tools with ease, from tensor methods and Young tableau, as for the part on symmetry, to the technical methods generally used to deal with the calculation QCD cross sections.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) Knowing methods for constructing the representations of SU(3) and SU(2)
OF 2) Understanding the role of symmetry principles in the construction of physical theories.
OF 3) Knowing methods for the calculation of elementary processes in QCD
OF 4) Knowing basics of hadron collider physics

B - Application skills
OF 5) Compute Kronecker products of representations of Casimir factors and `color factors` and constructions of SU(3) representations with tensor methods and Young Tableau
OF 6) Calculate scattering processes in QCD
OF 7) Calculation of some loop amplitudes in QCD with the method of dimensional regularization and of renormalization with counterterms.

C - Autonomy of judgment
OF 8) Ability to apply the knowledge base acquired to understand the modern developments in theoretical particle physics
OF 9) Being able to apply dimensional analysis reasonings and order of magnitude estimates.

D - Communication skills
OF 10) Ability to discuss about collider physics and QCD with rigor and understanding of the approximations.

E - Ability to learn
OF 11) Ability to read and understand independently more advanced texts and papers.
OF 12) Being able to discriminate between the various, sometimes confusing, conventions, notations and methods used in the literature.

Educational objectives

Formative targets:

The objectives of the course are to bring the student to a deep knowledge and understanding of the basic mathematical properties i) of the nonlinear wave propagation with or without dispersion or dissipation; ii) of the construction of nonlinear mathematical models of physical interest, through the multiscale method, like the soliton equations, and of the mathematical techniques to solve them, arriving to the introduction of current research topics in the theory of solitons and anomalous waves. At the end of the course the student must be able i) to apply the acquired methods to problems in nonlinear physics even different from those studied in the course, in fluid dynamics, nonlinear optics, theory of gravitation, etc .., solving typical problems of the nonlinear dynamics; ii) to integrate in autonomy the acquired knowledges through the suggested literature, to solve also problems of interest for him/her, and not investigated in the course. The student will have the ability to consult supplementary material, interesting scientific papers, having acquired the right knowledges and critical skill to evaluate their content and their potential benefits to his/her scientific interests. At last the student must be able to conceive and develop a research project in autonomy. In order to achieve these goals, we plan to involve the student, during the theoretical lectures and exercises, through general and specific questions related to the subject; or through the presentation in depth of some specific subject agreed with the teacher.

Educational objectives

SPECIFIC OBJECTIVES:
Knowledge and understanding:
The course, starting from the general principles of data analysis, will explore fundamental techniques and their applications in various scientific contexts. Methods of statistical analysis, modeling, and data interpretation will be covered, with particular attention to applications in gravitational wave research. Students will acquire the skills to apply the concepts learned rigorously, not only in the study of gravitational waves but also in various scientific fields, tackling data analysis in a versatile way applicable to different research areas.

Judgment autonomy:
Through active participation in the lessons and continuous interaction with the teacher, students will develop solid judgment autonomy, having the opportunity to constantly engage with the material and critically analyze the information acquired.

Communication skills, learning ability:
The acquisition of skills and tools for effective communication will be assessed both during the lectures and through the final exam, promoting the development of every student's communication abilities.

Educational objectives

KNOWLEDGE AND UNDERSTANDING
Upon completion of the course, the student will know the principles of special relativity, with particular reference to the link with classical mechanics, electromagnetism, the transformations of fields between inertial reference systems, the principles on which modern particle accelerators are based, the relativistic motion of charges in electric and magnetic fields and the functioning of linear accelerators, cyclotrons and synchrotrons
APPLICATION CAPABILITIES:
The student will be able to schematically design some devices used in accelerators, such as quadrupoles, and discuss the motion of the charges in these devices.
AUTONOMY OF JUDGMENT
The student will be able to determine the operating principles of a circular accelerator thanks to the acquired concepts of betatron and synchrotron motion and to independently use the simulation code ASTRA (A Space Charge Tracking Algorithm).
COMMUNICATION SKILLS
The student will be able to deal with topics related to particle accelerators using terms and concepts typical of this sector

Educational objectives

SPECIFIC OBJECTIVES:
A- Knowledge and understanding
OF 1) Starting from the experimental bases of gravitation, and the theoretical implications, the course focusses on gravitational wave detection. Two interlaces aspects will be illustrated, the experimental apparuses and data analysis technicques.
OF 2) This will give students the necessary preparation for a rigorous application of the acquired notions, not only for the topics inherent to the course, but for the broadest and more general field of experimental physics of fundamental interactions.
B - Application skills
OF 3) The student will be able to correctly interpret the experimental issues and the avancement of the apparatuses.
OF 4) The student will be able to apply techniques/metods of data analysis
C - Autonomy of judgment
OF 5) Thanks to the lesson attendance, and the persistent interaction with the lecturer, the student will develop an adequate autonomy of judgment and will critically analyze the acquired information.
D - Communication skills
OF 6) The acquisition of adequate skills and tools for communication will be verified both during the
lessons and during the final exam, contributing to the development of clear communication skills by the student.
E - Ability to learn
OF 7) The student will have the ability to evaluate and solve a broad range of data analysis issues.
OF 8) Ther student will be able to conceive and develop an experimental/theoretical project,
starting from the data acquisition, through the analysis of the collected data and outlining some conclusions via the related post-processing.

Educational objectives

GENERAL OBJECTIVES:
The course will cover the physics of particle detectors and particle accelerators. It will introduce the experimental techniques used in nuclear, particle physics and photon science, and describe the layout and functionality of modern experiments. History, operating principles of modern particle accelerators and applications in nuclear, sub-nuclear and medical physics will be treated as well.

Through classroom lectures, dedicated seminars held by experts and hands-on exercise sessions, the Detectors and Accelerators in Particle Physics course proposes:
- to deepen the knowledge of the interactions of elementary particles with matter;
- to analyze the functioning of the various detectors used for the detection of elementary particles in nuclear and subnuclear physics;
- to examine some current experiments of greater interest;
- to provide an introduction to the physics of particle accelerators by also presenting future projects;
- to teach how to design and simulate simple experimental using the Geant4 software library.

At the end of the course, students will be familiar with modern detection and particle acceleration methods in particle and applied physics. They will have the basis to understand the motivations and the functioning of the various parts of an experiment in high energy physics or instrumentation for the control of the beams in medical physics laboratories. This will include the ability to size and select detectors suitable for the purposes of the experiments to be examined or to be designed.
They will know how to describe measurements of ionization, position, energy, and momentum of particles, as well as particle identification and timing measurements. They will develop competence in quickly and critically acquiring information from publications other then textbooks.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) To know the fundamentals of particle detectors
OF 2) To know the fundamentals of particle accelerators
OF 3) To understand the language of the physics of particle detectors and accelerators

B - Application skills
OF 4) Ability to design, dimension and choose suitable detectors for a specific particle physics experiment
OF 5) Ability to implement a simple simulation setup with Geant4 for a particle detector
C - Autonomy of judgment
OF 6) To be able to analyze and evaluate the performance of a particle physics detectors
OF 7) To be able to analyze and evaluate the performance of a particle accelerator
D - Communication skills
OF 8) Being able to clearly communicate the operation and properties of a particle detector and of a particle accelerator, and their applicability in realistic contexts
OF 9) Being able to motivate the architectural choices behind a specific particle detector or accelerator design

E - Ability to learn
OF 8) Being able to learn alternative and more complex techniques
OF 9) Being able to implement existing techniques in an efficient, robust and reliable manner

Educational objectives

The aim of the course is to learn the experimental evidences and the
methodologies that led to the formulation of the Standard Model (SM) of
elementary particle physics, from the beginning of the discipline in the
30s and 40s of the last century until the formulation of the SM. The
course is closely linked to the theoretical courses of the first
semester and to the annual course of Laboratory.

At the end of the course the students have to:
1) know and be able to discuss the fundamental concepts of the SM
2) know the fundamental experiments that allowed the development of the SM
3) to have understood the main methodologies of the experimental
particle physics, both the technological and the statistical aspects.

Educational objectives

SPECIFIC OBJECTIVES:
Knowledge and understanding:
The course, starting from the general principles of data analysis, will explore fundamental techniques and their applications in various scientific contexts. Methods of statistical analysis, modeling, and data interpretation will be covered, with particular attention to applications in gravitational wave research. Students will acquire the skills to apply the concepts learned rigorously, not only in the study of gravitational waves but also in various scientific fields, tackling data analysis in a versatile way applicable to different research areas.

Judgment autonomy:
Through active participation in the lessons and continuous interaction with the teacher, students will develop solid judgment autonomy, having the opportunity to constantly engage with the material and critically analyze the information acquired.

Communication skills, learning ability:
The acquisition of skills and tools for effective communication will be assessed both during the lectures and through the final exam, promoting the development of every student's communication abilities.

Educational objectives

SPECIFIC OBJECTIVES:
A- Knowledge and understanding
OF 1) Starting from the experimental bases of gravitation, and the theoretical implications, the course focusses on gravitational wave detection. Two interlaces aspects will be illustrated, the experimental apparuses and data analysis technicques.
OF 2) This will give students the necessary preparation for a rigorous application of the acquired notions, not only for the topics inherent to the course, but for the broadest and more general field of experimental physics of fundamental interactions.
B - Application skills
OF 3) The student will be able to correctly interpret the experimental issues and the avancement of the apparatuses.
OF 4) The student will be able to apply techniques/metods of data analysis
C - Autonomy of judgment
OF 5) Thanks to the lesson attendance, and the persistent interaction with the lecturer, the student will develop an adequate autonomy of judgment and will critically analyze the acquired information.
D - Communication skills
OF 6) The acquisition of adequate skills and tools for communication will be verified both during the
lessons and during the final exam, contributing to the development of clear communication skills by the student.
E - Ability to learn
OF 7) The student will have the ability to evaluate and solve a broad range of data analysis issues.
OF 8) Ther student will be able to conceive and develop an experimental/theoretical project,
starting from the data acquisition, through the analysis of the collected data and outlining some conclusions via the related post-processing.

Educational objectives

A - Knowledge and understanding
OF 1) To know the Collider basic principles and the most important Physics resulta obtained in this field.
OF 2) To understand in which field of research are used the different kind of Colliders.
OF 3) To understand the bacis principles of Detectors used in the Colliders.

B - Application skills
OF 7) To be able to participate to a Collider Physics Experiment
OF 8) To be able to do the Data analysis of the Experiment.
OF 9) To be able to apply methods/techniques…

C - Autonomy of judgment
OF 10) To be able to read and understand a pubblication on Particle Physics
OF 11) To be able to integrate the knowledge acquired in order to carry on a research work in Particle Physics.

D - Communication skills
OF 13) To know how to communicate the results of his/her own research.

E - Ability to learn
OF 15) Have the ability to consult the sector specialised literature
OF 16) Have the ability to evaluate the last results obtained in the field.

Educational objectives

GENERAL OBJECTIVES:
To provide basics of Cosmology and of its links with Neutrino and Dark Matter Physics.
To provide phenomenological foundations of Neutrino and Dark Matter Physics.
To provide an overview of present and future experiments.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) Basic Cosmology
OF 2) Theoretical and phenomenological frameworks of Neutrino and Dark Matter searches.
OF 3) Main experiments in the field.
OF 4) Short and long terms goals in the field.

B - Application skills
OF 5) To be able to join research projects of the field.
OF 6) To be able to understand scientific discussions of the field.

C - Autonomy of judgment
OF 7) To be able to criticize current research directions.
OF 8) To be able to identify strenghts and weaknesses of different searches.

D - Communication skills
OF 9) T be able to bridge the communication between theoretical and experimental aspects.

E - Ability to learn
OF 10) Ability to understand the scientific material of the field.

Educational objectives

A - Knowledge and understanding
OF 1) Starting from the experimental bases of gravitation, and the theoretical implications, the course focusses on gravitational wave detection. Two interlaces aspects will be illustrated, the experimental apparuses and data analysis technicques.
OF 2) This will give students the necessary preparation for a rigorous application of the acquired notions, not only for the topics inherent to the course, but for the broadest and more general field of experimental physics of fundamental interactions.
B - Application skills
OF 3) The student will be able to correctly interpret the experimental issues and the avancement of the apparatuses.
OF 4) The student will be able to apply techniques/metods of data analysis
C - Autonomy of judgment
OF 5) Thanks to the lesson attendance, and the persistent interaction with the lecturer, the student will develop an adequate autonomy of judgment and will critically analyze the acquired information.
D - Communication skills
OF 6) The acquisition of adequate skills and tools for communication will be verified both during the
lessons and during the final exam, contributing to the development of clear communication skills by the student.
E - Ability to learn
OF 7) The student will have the ability to evaluate and solve a broad range of data analysis issues.
OF 8) Ther student will be able to conceive and develop an experimental/theoretical project,
starting from the data acquisition, through the analysis of the collected data and outlining some conclusions via the related post-processing.

Educational objectives

GENERAL OBJECTIVES:
The course aims to provide the necessary knowledge of the operating principles of the instrumentation used in biomedical research and diagnostics. In particular, the students study the interactions of ionizing and non-ionizing radiation with matter and learn how to exploit them in imaging techniques. The knowledge of radiography and tomography with X and gamma rays, with magnetic resonance and ultrasound is acquired.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) To know the fundamentals of radiation-material interactions in biomedicine.
OF 2) To learn about physical methods for imaging and the biological effects of radiation in medicine.
OF 3) To understand image reconstruction algorithms in diagnostics and research.
OF 4) To know the equipments used for imaging in biomedicine.
OF 5) To understand radiation detectors in medicine.
…
B - Application skills
OF 6) To Know how to deduce the response of the detectors used in biomedicine.
OF 7) To be able to solve problems related to the interaction of ionizing radiation and matter.
…
C - Autonomy of judgment
OF 8) To be able to integrate the knowledge acquired in order to apply them for diagnostics and research in the health sector.

D - Communication skills

E - Ability to learn
OF 9) Have the ability to consult scientific articles in order to independently investigate topics in the health sector.
OF 10) Be able to conceive and develop a related diagnostic imaging project in biomedicine.

Educational objectives

A - Knowledge and understanding
OF 1) Knowledge of the features of cosmic rays
OF 2) Knowledge of the nature and properties of the elementary particles
OF 3) Knowledge of the nature and features of collisons
OF 4) Knowledge of the trasport equations of primary and secondary cosmic rays in the
atmosphere and the development of showers
OF 5) Understand the differential flux and mass composition of the primary cosmic rays
OF 6) Knowledge of the problem of the ultra high energy cosmic rays
OF 7) Knowledge of the the first and second order Fermi acceleration mechanism
B – Application skills
OF 8) Be able to deduce the basic issues of astroparticle physics starting by using the
observational techniques
OF 9) Be able to apply the propagation of ultra high energy particles such as protons, photons,
neeutrinos and heavy nuclei
OF 10) Be able to apply the first and second order Fermi acceleration mechanism
OF 11) Be able to deduce the limits of the observational techniques in use in the different
esperiments
C - Autonomy of judgment
OF 12) Be able to evaluate the nature of the different interacting particles in a specif process
OF 13) Be able to evaluate the observational methodologies for the different experiments
OF 14) Be able to evaluate every aspect of the system
OF 15) Be able to suggest the techniques to perform a scientific evaluation of the system
D - Communication skills
OF 16) Know how to describe the nature of physical processes to workers without scientific
training
OF 17) Know how to communicate physical techniques for a complete study of the system
E - Ability to learn
OF 18) Have the ability to consult scientific literature and physical methods
OF 19) Have the ability to evaluate technical descriptions for specific physical processes

Educational objectives

GENERAL OBJECTIVES: Understanding the fundamental optical and transport properties of semiconductors and using these properties in the main electronic and opto-electronic devices.

SPECIFIC OBJECTIVES:
A – Knowledge and understanding
OF 1) To know the fundamental electronic properties of semiconductors and how they derive from their crystalline structure and chemical composition.
OF 2) To understand how the fundamental electronic properties of semiconductors can be modified by material nanostructuring.
OF 3) To know the main charge transport phenomena in semiconductors.
OF 4) To know the main processes of interaction of light with semiconductors and related phenomena.
OF 5) Based on the previous points, learning the operating principles of the most common electronic and optoelectronic devices based on semiconductor materials.

B - APPLICATION SKILLS
OF 6) To know in general how to determine which semiconductor materials can be used to fabricate devices with specific characteristics.
OF 7) To know how to predict the effects of electromagnetic fields on the transport and optical properties of semiconductors.
OF 8) To be able to select a semiconductor device for the measurement of given quantities.
C – Autonomy of judgement
OF 9) To determine the connections between the properties of a semiconductor and the characteristics of a device.
OF 10) To be able to integrate the knowledge acquired in order to exploit it in the more general context of device applications of semiconductor materials.
D – Communication skills
OF 11) To know how to explain the fundamental reasons behind the functioning principle of a device.
OF 12) To know how to justify the choice of a semiconductor material for carrying out specific applications.
E – Ability to learn
OF 13) To acquire the ability to independently read and understand scientific texts and technical articles based on the topics covered in the course.
OF 14) To have the ability to choose and identify an appropriate device depending on the use.

Educational objectives

A - Knowledge and understanding
OF 1) Knowledge of the features of cosmic rays
OF 2) Knowledge of the nature and properties of the elementary particles
OF 3) Knowledge of the nature and features of collisons
OF 4) Knowledge of the trasport equations of primary and secondary cosmic rays in the
atmosphere and the development of showers
OF 5) Understand the differential flux and mass composition of the primary cosmic rays
OF 6) Knowledge of the problem of the ultra high energy cosmic rays
OF 7) Knowledge of the the first and second order Fermi acceleration mechanism
B – Application skills
OF 8) Be able to deduce the basic issues of astroparticle physics starting by using the
observational techniques
OF 9) Be able to apply the propagation of ultra high energy particles such as protons, photons,
neeutrinos and heavy nuclei
OF 10) Be able to apply the first and second order Fermi acceleration mechanism
OF 11) Be able to deduce the limits of the observational techniques in use in the different
esperiments
C - Autonomy of judgment
OF 12) Be able to evaluate the nature of the different interacting particles in a specif process
OF 13) Be able to evaluate the observational methodologies for the different experiments
OF 14) Be able to evaluate every aspect of the system
OF 15) Be able to suggest the techniques to perform a scientific evaluation of the system
D - Communication skills
OF 16) Know how to describe the nature of physical processes to workers without scientific
training
OF 17) Know how to communicate physical techniques for a complete study of the system
E - Ability to learn
OF 18) Have the ability to consult scientific literature and physical methods
OF 19) Have the ability to evaluate technical descriptions for specific physical processes

Educational objectives

A - Knowledge and understanding
OF 1) To know the Collider basic principles and the most important Physics resulta obtained in this field.
OF 2) To understand in which field of research are used the different kind of Colliders.
OF 3) To understand the bacis principles of Detectors used in the Colliders.

B - Application skills
OF 7) To be able to participate to a Collider Physics Experiment
OF 8) To be able to do the Data analysis of the Experiment.
OF 9) To be able to apply methods/techniques…

C - Autonomy of judgment
OF 10) To be able to read and understand a pubblication on Particle Physics
OF 11) To be able to integrate the knowledge acquired in order to carry on a research work in Particle Physics.

D - Communication skills
OF 13) To know how to communicate the results of his/her own research.

E - Ability to learn
OF 15) Have the ability to consult the sector specialised literature
OF 16) Have the ability to evaluate the last results obtained in the field.

Educational objectives

A - Knowledge and understanding
OF 1) Starting from the experimental bases of gravitation, and the theoretical implications, the course focusses on gravitational wave detection. Two interlaces aspects will be illustrated, the experimental apparuses and data analysis technicques.
OF 2) This will give students the necessary preparation for a rigorous application of the acquired notions, not only for the topics inherent to the course, but for the broadest and more general field of experimental physics of fundamental interactions.
B - Application skills
OF 3) The student will be able to correctly interpret the experimental issues and the avancement of the apparatuses.
OF 4) The student will be able to apply techniques/metods of data analysis
C - Autonomy of judgment
OF 5) Thanks to the lesson attendance, and the persistent interaction with the lecturer, the student will develop an adequate autonomy of judgment and will critically analyze the acquired information.
D - Communication skills
OF 6) The acquisition of adequate skills and tools for communication will be verified both during the
lessons and during the final exam, contributing to the development of clear communication skills by the student.
E - Ability to learn
OF 7) The student will have the ability to evaluate and solve a broad range of data analysis issues.
OF 8) Ther student will be able to conceive and develop an experimental/theoretical project,
starting from the data acquisition, through the analysis of the collected data and outlining some conclusions via the related post-processing.

Educational objectives

GENERAL OBJECTIVES:
The course aims to provide the necessary knowledge of the operating principles of the instrumentation used in biomedical research and diagnostics. In particular, the students study the interactions of ionizing and non-ionizing radiation with matter and learn how to exploit them in imaging techniques. The knowledge of radiography and tomography with X and gamma rays, with magnetic resonance and ultrasound is acquired.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) To know the fundamentals of radiation-material interactions in biomedicine.
OF 2) To learn about physical methods for imaging and the biological effects of radiation in medicine.
OF 3) To understand image reconstruction algorithms in diagnostics and research.
OF 4) To know the equipments used for imaging in biomedicine.
OF 5) To understand radiation detectors in medicine.
…
B - Application skills
OF 6) To Know how to deduce the response of the detectors used in biomedicine.
OF 7) To be able to solve problems related to the interaction of ionizing radiation and matter.
…
C - Autonomy of judgment
OF 8) To be able to integrate the knowledge acquired in order to apply them for diagnostics and research in the health sector.

D - Communication skills

E - Ability to learn
OF 9) Have the ability to consult scientific articles in order to independently investigate topics in the health sector.
OF 10) Be able to conceive and develop a related diagnostic imaging project in biomedicine.

Educational objectives

GENERAL OBJECTIVES:
To provide basics of Cosmology and of its links with Neutrino and Dark Matter Physics.
To provide phenomenological foundations of Neutrino and Dark Matter Physics.
To provide an overview of present and future experiments.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) Basic Cosmology
OF 2) Theoretical and phenomenological frameworks of Neutrino and Dark Matter searches.
OF 3) Main experiments in the field.
OF 4) Short and long terms goals in the field.

B - Application skills
OF 5) To be able to join research projects of the field.
OF 6) To be able to understand scientific discussions of the field.

C - Autonomy of judgment
OF 7) To be able to criticize current research directions.
OF 8) To be able to identify strenghts and weaknesses of different searches.

D - Communication skills
OF 9) T be able to bridge the communication between theoretical and experimental aspects.

E - Ability to learn
OF 10) Ability to understand the scientific material of the field.

Educational objectives

GENERAL OBJECTIVES:

This course will introduce the student to the most important concepts, ideas and tools of quantum field theory which has become the universal framework to describe all fundamental forces in nature. The student will understand how to construct field theories, quantize them in the presence of interactions and how to apply advanced techniques of regularization and renormalisation. Some special regard will be devoted to functional methods. The course will include the mathematical structure of non-Abelian gauge theories and their role in our present understanding of fundamental forces. The student will also have an elementary understanding of anomalies and their physical consequences in nature.

SPECIFIC OBJECTIVES:

A - Knowledge and understanding

The goal is for students to develop a critical understanding of the topics covered during the course, both as regards the purely theoretical aspects and in relation to the applications to different physical phenomena, and that they develop an adequate knowledge of the methods applied in theoretical physics, with particular reference to the methods usually used to conduct research in this sector.

B - Application skills

Alongside understanding the topics and methods used during the lessons, one of the objectives of the course is to enable students to apply those same methods to new problems, be they study or research.

C - Autonomy of judgment

One of the main objectives of the course is for students to develop critical skills with respect to the topics covered. They are often encouraged to follow other paths (than those followed during the lectures) for the achievement of results, or to propose interpretations or readings different from those presented by the teacher of the same results. Often during the lessons students are asked to make suggestions or make estimates in relation to specific calculations, with the aim of encouraging their autonomy of thought and their ability to make choices when confronted with delicate steps.

D - Communication skills

The course aims to increase students' communication skills, providing them with methodological tools that allow them to improve their ability to discuss in an original way topics related to theoretical and applicative aspects of quantum field theory.

E - Ability to learn

One of the most important objectives of the course is to provide students with a methodology that allows them to have access to a continuous updating of knowledge, trying in particular to increase their ability to deal with specialized literature.

Educational objectives

GENERAL OBJECTIVES: Understanding the fundamental optical and transport properties of semiconductors and using these properties in the main electronic and opto-electronic devices.

SPECIFIC OBJECTIVES:
A – Knowledge and understanding
OF 1) To know the fundamental electronic properties of semiconductors and how they derive from their crystalline structure and chemical composition.
OF 2) To understand how the fundamental electronic properties of semiconductors can be modified by material nanostructuring.
OF 3) To know the main charge transport phenomena in semiconductors.
OF 4) To know the main processes of interaction of light with semiconductors and related phenomena.
OF 5) Based on the previous points, learning the operating principles of the most common electronic and optoelectronic devices based on semiconductor materials.

B - APPLICATION SKILLS
OF 6) To know in general how to determine which semiconductor materials can be used to fabricate devices with specific characteristics.
OF 7) To know how to predict the effects of electromagnetic fields on the transport and optical properties of semiconductors.
OF 8) To be able to select a semiconductor device for the measurement of given quantities.
C – Autonomy of judgement
OF 9) To determine the connections between the properties of a semiconductor and the characteristics of a device.
OF 10) To be able to integrate the knowledge acquired in order to exploit it in the more general context of device applications of semiconductor materials.
D – Communication skills
OF 11) To know how to explain the fundamental reasons behind the functioning principle of a device.
OF 12) To know how to justify the choice of a semiconductor material for carrying out specific applications.
E – Ability to learn
OF 13) To acquire the ability to independently read and understand scientific texts and technical articles based on the topics covered in the course.
OF 14) To have the ability to choose and identify an appropriate device depending on the use.

Educational objectives

A - Knowledge and understanding
OF 1) Knowing the theoretical foundations and the phenomenological aspects of the Standard Model
OF 2) Knowing the theoretical and phenomenological aspects of the spontaneous breaking of the electroweak symmetry and the related precision tests.
OF 3) Knowing the main aspects of flavour physics in the hadronic sector and in the leptonic sector.
OF 4) Understanding the field theoretical methods used in the context of high-energy physics

B - Application skills
OF 5) Knowing how to identify the main aspects in the calculation of Standard Model predictions of physical observables. Knowing how to estimate the dependence of physical quantities on the fundamental parameters using dimensional analysis.
OF 6) Knowing how to identify the relevant symmetries in the various phenomenologcial applications and how to deduce their consequences.
OF 7) Being able to use field theoretical methods relevant to high-energy physics

C - Autonomy of judgment
OF 8) The student will have to learn how to evaluate the correctness of the logical reasoning used in the discussion of the various phenomenological applications and in the proofs of theorems.
OF 9) The regular assignment of exercises will encourage the habit of self-assessment.
OF 10) The extensive literature suggested will encourage individual initiative to deepen the study of some of the topics covered.

D - Communication skills
OF 11) The acquisition of adequate skills and tools for communication will be verified during the evaluation test. The oral exam requires the student to express herself/himself with scientific language and follow a rigorous logic in reasoning.

E - Ability to learn
OF 12) The work required for this course stimulates the development of a flexible mentality, useful both for more advanced scientific studies and in the context of various workplaces.

Educational objectives

To form the students on the following topics:
- linear response theory in solids
- light-matter interaction: quantum description of optical and infrared
spectroscopies
- impact of electron electron interaction on excitations: plasmon and
excitons
- charge transport in solids
- topological properties of solids

Educational objectives

GENERAL OBJECTIVES:
The course aims to introduce the foundations of Superconductivity and Superfluidity. A preliminary part will be devoted to the phenomenological London and Ginzburg-Landau theories. The latter will be used to introduce the more general topic of spontaneous symmetry breaking in second-order phase transition, and the Anderson-Higgs mechanism for superconductivity. After discussion of the second-quantization for many-body fermionic and bosonic systems the focus will be on the microscopic models for superconductors (BCS Bardeen_Cooper e Schrieffer theory) and superfluids.
The final part will consist in a brief overview of current research topics on unconventional superconductors.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) To know the basis of the superconducting phenomenon, its phenomenological and microscopic description and its experimental applications
OF 2) To understand key concepts as spontaneous symmetry breaking and order parametr for a phase transition, with particular emphasis on continous symmetries.
OF 3) To know basic applications of second quantization to fermionic and bosonic many-particle systems
B - Application skills
OF 4) To be able to describe the superfluid phenomen both for fermions and bosons, and its theoretical and experimental implications
C - Autonomy of judgment
OF 5) To be able to integrate the knowledge acquired in order to apply in the more general context of unconventional superconduvtivity and interacting fermionic systems
E - Ability to learn
OF 6) Have the ability to read scientific papers in order to further explore some of the topics introduced during the course.

Educational objectives

GENERAL OBJECTIVES:
The aim of the course is to teach the main paradigms in many-body systems, particularly of fermionic systems, like electrons in metals, and to give an introduction to the methods of field theory in conndensed matter. At the end of the course the student should have acquired both technical competences (second quantization, Green function and Feynman diagrams at T=0 and T>0, response functions) and the physical understanding of the simplest approximations used to describe the many-body effects. In general the student should be able to understand both the language and the issues of modern research in correlated systems.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) Basic concepts of Landau Fermi liquid theory, the fundamental paradigm of the metallic state
OF 2) Properties of the Green functions and their physical meaning
OF 3) Interaction representation. S matrix. Wick's theorem and Feynman diagrams.
OF 4) Self-energy and Dyson equation. Hartree-Fock approximation, RPA approximation
OF 5) Linear response theory; response function. Analytic properties. Reactive and absorptive part.
OF 6) Kramers-Kronig relations. Kubo formula Fluctuation and dissipation theorem
B - Application skills
OF 7) The second objective is to prepare the students to actively solve problems in physics where MB theory concepts are required. This will happen at first with problems structured within a conceptual scheme similar to the ones discussed and applied during the course. However, as their preparation progresses, students are also expected to use MB concepts for solving new problems in different applications.
C - Autonomy of judgment
OF 8) The third and more ambitious objective is to teach the students to think using concepts and methods from MB theory as a powerful problem solving tool in physics.
D - Communication skills
OF 9) Besides having a clear understanding of the new acquired concepts in MB theory, the students should correspondingly acquire the ability to communicate and transmit these concepts in a clear and direct way.
E - Ability to learn
OF 10) The students should become able to read and understand scientific books and articles where MB concepts are involved and should be able to deepen autonomously their knowledge in this field.

Educational objectives

To form the students on the following topics:
- linear response theory in solids
- light-matter interaction: quantum description of optical and infrared
spectroscopies
- impact of electron electron interaction on excitations: plasmon and
excitons
- charge transport in solids
- topological properties of solids

Educational objectives

A - Knowledge and understanding
OF 1) To possess a basic knowledge of complexity science, i.e. the collective properties that emerge with a large number of interacting components (atoms, particles or bacteria in a physical or biological context, or people, machines or businesses in a socio-economic context).
OF 2) Understanding the mechanisms underlying the emergence of complex macroscopic properties from knowledge of microscopic mechanisms.
OF 3) Mastering the basic toolbox of a complexity scientist: information theory, network theory, scale invariance and critical phenomena, properties of dynamical systems, agent models.
B - Application skills
OF 4) Knowing how to devise simple models for complex phenomenologies.
OF 5) Being able to tackle complex problems analytically or computationally, translating research questions into concrete solution and verification actions.
OF 6) Being able to apply the techniques and methods learnt also outside the areas covered in the course.
OF 7) Integrating the knowledge acquired in order to formalise problems and obtain results and predictions of increasing accuracy.
C - Autonomy of judgment
OF 8) Being able to analyse phenomena, also through the acquisition of data and evidence, that fall within the scope of complexity and identify their essential elements.
OF 9) Being able to synthesise phenomenologies in order to be able to distill relevant and relevant questions.
OF 10) Being able to identify interesting new research directions.
D - Communication skills
OF 11) Being able to communicate complex issues in a simple way, focusing on the essential elements and revealing cause-effect relationships as far as possible.
OF 12) Being able to organise a coherent, profound yet comprehensible presentation.
OF 13) Knowing how to express one's thoughts in a way that stimulates group work and interaction with colleagues.
E - Ability to learn
OF 14) Have the ability to consult reference texts and articles.
OF 15) Being able to assess the relevance of results, their place in the scientific panorama of reference and their potential importance for the research topics of interest.
OF 16) Being able to design and develop a research project, identifying the main objectives and the possible paths to reach them.

Educational objectives

GENERAL OBJECTIVES:

The Surface Physics and Nanostructures course aims to provide the knowledge of the structural properties of solid systems at low dimensional scale and to understand their characteristics from the point of view of both electronic and vibrational degrees of freedom. The optical properties of nanostructured semiconductor systems and magnetic properties of nanostructured metal systems will then be analyzed.
At the end of the course, students will be able to transpose the knowledge of 3D solid state physics to two-dimensional and one-dimensional systems and have an in-depth knowledge of the frontier topics in nanosciences. These acquisitions will be verified also thanks to the presentation of the topics in seminars held by the students.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) To know the properties of low-dimensional solid systems
OF 2) To understand the effects of reduced dimensionality
OF 3) To know the most advanced techniques for studying the low-dimensional systems
B - Application skills
OF 4) To be able to deduce the properties of a surface or a nanostructure
OF 5) To be able to choose the correct technqiue to investigate a surface or a nanostructure
C - Autonomy of judgment
OF 6) To be able to autonomously individuate an experiment on low-dimensional systems
OF 7) To be able to integrate the acquired knowledge so to be able to face a scientific problem associated to low-dimensional systems
D - Communication skills
OF 8) To know how to communicate the properties of a low-dimensional system
OF 9) To be able to communicate the advantages of an advanced investigation

E - Ability to learn
OF 10) To have the ability to consult the specific scientific literature
OF 11) To be able to evaluate the specific scientific literature
OF 12) To be able to design and plan an experiment on low dimensional systems

Educational objectives

GENERAL OBJECTIVES:
The course aims to introduce the foundations of Superconductivity and Superfluidity. A preliminary part will be devoted to the phenomenological London and Ginzburg-Landau theories. The latter will be used to introduce the more general topic of spontaneous symmetry breaking in second-order phase transition, and the Anderson-Higgs mechanism for superconductivity. After discussion of the second-quantization for many-body fermionic and bosonic systems the focus will be on the microscopic models for superconductors (BCS Bardeen_Cooper e Schrieffer theory) and superfluids.
The final part will consist in a brief overview of current research topics on unconventional superconductors.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) To know the basis of the superconducting phenomenon, its phenomenological and microscopic description and its experimental applications
OF 2) To understand key concepts as spontaneous symmetry breaking and order parametr for a phase transition, with particular emphasis on continous symmetries.
OF 3) To know basic applications of second quantization to fermionic and bosonic many-particle systems
B - Application skills
OF 4) To be able to describe the superfluid phenomen both for fermions and bosons, and its theoretical and experimental implications
C - Autonomy of judgment
OF 5) To be able to integrate the knowledge acquired in order to apply in the more general context of unconventional superconduvtivity and interacting fermionic systems
E - Ability to learn
OF 6) Have the ability to read scientific papers in order to further explore some of the topics introduced during the course.

Educational objectives

GENERAL OBJECTIVES:

This course will introduce the student to the most important concepts, ideas and tools of quantum field theory which has become the universal framework to describe all fundamental forces in nature. The student will understand how to construct field theories, quantize them in the presence of interactions and how to apply advanced techniques of regularization and renormalisation. Some special regard will be devoted to functional methods. The course will include the mathematical structure of non-Abelian gauge theories and their role in our present understanding of fundamental forces. The student will also have an elementary understanding of anomalies and their physical consequences in nature.

SPECIFIC OBJECTIVES:

A - Knowledge and understanding

The goal is for students to develop a critical understanding of the topics covered during the course, both as regards the purely theoretical aspects and in relation to the applications to different physical phenomena, and that they develop an adequate knowledge of the methods applied in theoretical physics, with particular reference to the methods usually used to conduct research in this sector.

B - Application skills

Alongside understanding the topics and methods used during the lessons, one of the objectives of the course is to enable students to apply those same methods to new problems, be they study or research.

C - Autonomy of judgment

One of the main objectives of the course is for students to develop critical skills with respect to the topics covered. They are often encouraged to follow other paths (than those followed during the lectures) for the achievement of results, or to propose interpretations or readings different from those presented by the teacher of the same results. Often during the lessons students are asked to make suggestions or make estimates in relation to specific calculations, with the aim of encouraging their autonomy of thought and their ability to make choices when confronted with delicate steps.

D - Communication skills

The course aims to increase students' communication skills, providing them with methodological tools that allow them to improve their ability to discuss in an original way topics related to theoretical and applicative aspects of quantum field theory.

E - Ability to learn

One of the most important objectives of the course is to provide students with a methodology that allows them to have access to a continuous updating of knowledge, trying in particular to increase their ability to deal with specialized literature.

Educational objectives

To form the students on the following topics:
- linear response theory in solids
- light-matter interaction: quantum description of optical and infrared
spectroscopies
- impact of electron electron interaction on excitations: plasmon and
excitons
- charge transport in solids
- topological properties of solids

Educational objectives

GENERAL OBJECTIVES:
The course aims to provide the necessary knowledge of the operating principles of the instrumentation used in biomedical research and diagnostics. In particular, the students study the interactions of ionizing and non-ionizing radiation with matter and learn how to exploit them in imaging techniques. The knowledge of radiography and tomography with X and gamma rays, with magnetic resonance and ultrasound is acquired.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) To know the fundamentals of radiation-material interactions in biomedicine.
OF 2) To learn about physical methods for imaging and the biological effects of radiation in medicine.
OF 3) To understand image reconstruction algorithms in diagnostics and research.
OF 4) To know the equipments used for imaging in biomedicine.
OF 5) To understand radiation detectors in medicine.
…
B - Application skills
OF 6) To Know how to deduce the response of the detectors used in biomedicine.
OF 7) To be able to solve problems related to the interaction of ionizing radiation and matter.
…
C - Autonomy of judgment
OF 8) To be able to integrate the knowledge acquired in order to apply them for diagnostics and research in the health sector.

D - Communication skills

E - Ability to learn
OF 9) Have the ability to consult scientific articles in order to independently investigate topics in the health sector.
OF 10) Be able to conceive and develop a related diagnostic imaging project in biomedicine.

Educational objectives

GENERAL OBJECTIVES:
The aim of the course is to teach the main paradigms in many-body systems, particularly of fermionic systems, like electrons in metals, and to give an introduction to the methods of field theory in conndensed matter. At the end of the course the student should have acquired both technical competences (second quantization, Green function and Feynman diagrams at T=0 and T>0, response functions) and the physical understanding of the simplest approximations used to describe the many-body effects. In general the student should be able to understand both the language and the issues of modern research in correlated systems.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) Basic concepts of Landau Fermi liquid theory, the fundamental paradigm of the metallic state
OF 2) Properties of the Green functions and their physical meaning
OF 3) Interaction representation. S matrix. Wick's theorem and Feynman diagrams.
OF 4) Self-energy and Dyson equation. Hartree-Fock approximation, RPA approximation
OF 5) Linear response theory; response function. Analytic properties. Reactive and absorptive part.
OF 6) Kramers-Kronig relations. Kubo formula Fluctuation and dissipation theorem
B - Application skills
OF 7) The second objective is to prepare the students to actively solve problems in physics where MB theory concepts are required. This will happen at first with problems structured within a conceptual scheme similar to the ones discussed and applied during the course. However, as their preparation progresses, students are also expected to use MB concepts for solving new problems in different applications.
C - Autonomy of judgment
OF 8) The third and more ambitious objective is to teach the students to think using concepts and methods from MB theory as a powerful problem solving tool in physics.
D - Communication skills
OF 9) Besides having a clear understanding of the new acquired concepts in MB theory, the students should correspondingly acquire the ability to communicate and transmit these concepts in a clear and direct way.
E - Ability to learn
OF 10) The students should become able to read and understand scientific books and articles where MB concepts are involved and should be able to deepen autonomously their knowledge in this field.

Educational objectives

A - Knowledge and understanding
OF 1) To possess a basic knowledge of complexity science, i.e. the collective properties that emerge with a large number of interacting components (atoms, particles or bacteria in a physical or biological context, or people, machines or businesses in a socio-economic context).
OF 2) Understanding the mechanisms underlying the emergence of complex macroscopic properties from knowledge of microscopic mechanisms.
OF 3) Mastering the basic toolbox of a complexity scientist: information theory, network theory, scale invariance and critical phenomena, properties of dynamical systems, agent models.
B - Application skills
OF 4) Knowing how to devise simple models for complex phenomenologies.
OF 5) Being able to tackle complex problems analytically or computationally, translating research questions into concrete solution and verification actions.
OF 6) Being able to apply the techniques and methods learnt also outside the areas covered in the course.
OF 7) Integrating the knowledge acquired in order to formalise problems and obtain results and predictions of increasing accuracy.
C - Autonomy of judgment
OF 8) Being able to analyse phenomena, also through the acquisition of data and evidence, that fall within the scope of complexity and identify their essential elements.
OF 9) Being able to synthesise phenomenologies in order to be able to distill relevant and relevant questions.
OF 10) Being able to identify interesting new research directions.
D - Communication skills
OF 11) Being able to communicate complex issues in a simple way, focusing on the essential elements and revealing cause-effect relationships as far as possible.
OF 12) Being able to organise a coherent, profound yet comprehensible presentation.
OF 13) Knowing how to express one's thoughts in a way that stimulates group work and interaction with colleagues.
E - Ability to learn
OF 14) Have the ability to consult reference texts and articles.
OF 15) Being able to assess the relevance of results, their place in the scientific panorama of reference and their potential importance for the research topics of interest.
OF 16) Being able to design and develop a research project, identifying the main objectives and the possible paths to reach them.

Educational objectives

GENERAL OBJECTIVES:
This course will introduce students to the theory of classical and quantum information; elements of the algorithmic complexity theory; quantum computation and simulation; quantum cryptography. The student will study different experimental platforms to implement the protocols previously introduced.
At the end of the course, the student will be able, with a critical and analytical spirit, to formalize and analyze protocols of quantum communication and quantum computation. The ability to translate a quantum information processing task into an experimental platform will be developed, identifying its strengths and weaknesses.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1)To understand the fundamentals of information theory
OF 2) To understand the theory of quantum information
OF 3) To understand the language of quantum technologues

B - Application skills
OF 4) To be able to derive the evolution of a quantum circuit
OF 5) To be able to derive the evolution of an open quantum system
OF 6) To be able to model the different sources of noise present in a quantum information protocol
OF 7) To be able to define how to experimentally realize a quantum communication protocol
C - Autonomy of judgment
OF 8) To be able to exploit the knowledge acquired in quantum information for the implementation with different quantum technologies
D - Communication skills
OF 9) To know how to communicate in written reports an advanced concept
OF 10) To know how to present a recent research activity in the framework of quantum technologies
E - Ability to learn
OF 11) To be able to read independently scientific texts and articles in order to elaborate on the topics introduced in the course.

Educational objectives

GENERAL OBJECTIVES: Understanding the fundamental optical and transport properties of semiconductors and using these properties in the main electronic and opto-electronic devices.

SPECIFIC OBJECTIVES:
A – Knowledge and understanding
OF 1) To know the fundamental electronic properties of semiconductors and how they derive from their crystalline structure and chemical composition.
OF 2) To understand how the fundamental electronic properties of semiconductors can be modified by material nanostructuring.
OF 3) To know the main charge transport phenomena in semiconductors.
OF 4) To know the main processes of interaction of light with semiconductors and related phenomena.
OF 5) Based on the previous points, learning the operating principles of the most common electronic and optoelectronic devices based on semiconductor materials.

B - APPLICATION SKILLS
OF 6) To know in general how to determine which semiconductor materials can be used to fabricate devices with specific characteristics.
OF 7) To know how to predict the effects of electromagnetic fields on the transport and optical properties of semiconductors.
OF 8) To be able to select a semiconductor device for the measurement of given quantities.
C – Autonomy of judgement
OF 9) To determine the connections between the properties of a semiconductor and the characteristics of a device.
OF 10) To be able to integrate the knowledge acquired in order to exploit it in the more general context of device applications of semiconductor materials.
D – Communication skills
OF 11) To know how to explain the fundamental reasons behind the functioning principle of a device.
OF 12) To know how to justify the choice of a semiconductor material for carrying out specific applications.
E – Ability to learn
OF 13) To acquire the ability to independently read and understand scientific texts and technical articles based on the topics covered in the course.
OF 14) To have the ability to choose and identify an appropriate device depending on the use.

Educational objectives

GENERAL OBJECTIVES:
The main objective of the course is to illustrate the characteristics of some of the best known disordered models and to introduce the approximations and analytical techniques that allow their study in statistical mechanics.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) To know the main disordered models, such as dilute ferromagnets, ferromagnets with random external field, and spin glasses
OF 2) To understand the different physical behaviors that arise as a result of the introduction of quenched disorder (slowing down of the dynamics, metastability, presence of many thermodynamic states).
OF 3) To know the main techniques of statistical mechanics (mean-field approximations, replica and cavity methods) that allow the analytical study of models with disorder.

B - Application skills
OF 4) To know how to apply an analytical technique (mean-field approximation, replica and cavity method) to a given Hamiltonian to study its physical behavior.
C - Autonomy of judgment
OF 5) Be able to recognize to which class of disordered systems a given Hamiltonian belongs.

D - Communication skills
OF 6) Ability to present the course topics orally in a non-technical language that allows understanding even by those who have not yet taken the course.
E - Ability to learn
OF 7) To be able to read scientific texts and articles in order to independently investigate the topics introduced during the course.

Educational objectives

GENERAL OBJECTIVES:

The Surface Physics and Nanostructures course aims to provide the knowledge of the structural properties of solid systems at low dimensional scale and to understand their characteristics from the point of view of both electronic and vibrational degrees of freedom. The optical properties of nanostructured semiconductor systems and magnetic properties of nanostructured metal systems will then be analyzed.
At the end of the course, students will be able to transpose the knowledge of 3D solid state physics to two-dimensional and one-dimensional systems and have an in-depth knowledge of the frontier topics in nanosciences. These acquisitions will be verified also thanks to the presentation of the topics in seminars held by the students.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) To know the properties of low-dimensional solid systems
OF 2) To understand the effects of reduced dimensionality
OF 3) To know the most advanced techniques for studying the low-dimensional systems
B - Application skills
OF 4) To be able to deduce the properties of a surface or a nanostructure
OF 5) To be able to choose the correct technqiue to investigate a surface or a nanostructure
C - Autonomy of judgment
OF 6) To be able to autonomously individuate an experiment on low-dimensional systems
OF 7) To be able to integrate the acquired knowledge so to be able to face a scientific problem associated to low-dimensional systems
D - Communication skills
OF 8) To know how to communicate the properties of a low-dimensional system
OF 9) To be able to communicate the advantages of an advanced investigation

E - Ability to learn
OF 10) To have the ability to consult the specific scientific literature
OF 11) To be able to evaluate the specific scientific literature
OF 12) To be able to design and plan an experiment on low dimensional systems

Educational objectives

GENERAL OBJECTIVES:
The course is an advanced module aimed at guiding the students through a journey at the boundary between statistical physics and machine learning by introducing advanced concepts of equilibrium and out of equilibrium statistical mechanics and by illustrating their applications to learning models and development of artificial intelligence.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) To acquire the main methods of statistical mechanics, probability and information theory relevant to applications in machine learning and inference, such as the replica approach, message passing, mutual information, data compression, Bayesian approaches
OF 2) To understand the different physical behaviour shown by inference and artificial learning procedures (curse of dimensionality, metastability, presence of multiple thermodynamic states)
B - Application skills
OF 3) To know how to apply an analytical technique to a given inference or learning setting to study its physical behavior
C - Autonomy of judgment
OF 4) Be able to recognize to which class of disordered systems a given inference or learning setting belongs
D - Communication skills
OF 5) Ability to learn from oral presentation of research results on topics similar to those introduced during the course
OF 6) Ability to present the course topics orally in a non-technical language that allows understanding even by those who have not yet taken the course
E - Ability to learn
OF 7) To be able to read scientific texts and articles in order to independently investigate the topics introduced during the course

Educational objectives

A - Knowledge and understanding
OF 1) To know the fundamentals of the theory of stochastic processes, discrete and continuous, and thier formal framework in terms of resolution of Chapman-Kolmogorov, Fokker-Planck and master equations.
OF 2) To understand the similarities with the properties of equations already known to the students (like Schroedinger equation) and to learn equation resolution methods using operational calculus.
OF 3) To know the formalism of stochastic integration of stochastic differential equations and the connection to the Fokker-Planck partial differential equation.
B - Application skills
OF 4) To deduce physical properties of systems from the analysis of the stochastic equations.
OF 5) To apply newly learned methods to the estimate of first passage times and to the consequences of Arrhenius law on relaxation towards equilibrium in systems with rough potential landscapes.
OF 6) To apply methods and techniques to systems of different nature at and off equilibrium (viscous liquids, wave systmes, glassy systems, lasers).
C - Autonomy of judgment
OF 7) To be able to integrate acquired knwoledge and apply it also to cases not explicitly treated in the course.
OF 8) To be able to connect acquired knowledge to previous one, formalizing known concepts and connetcing them to more complex cases.
D - Communication skills
OF 9) To know how to orally present a demonstration procedure or an application assessing the most relevant and clarifying steps and their meaning.
E - Ability to learn
OF 10) To be able to consult diferrent textbooks and scientifc papers to the aim of autonomously deepening some of the arguments covered by the course.
OF 11) To be able to evaluate the effectiveness of the various studied approaches in relation to the treated problems.

Educational objectives

GENERAL OBJECTIVES
The course “Advanced Optical Techniques and Applications” aims to provide the necessary knowledge on optical and photonic techniques that are most used in the field of applied physics. In particular, the sources of electromagnetic radiation, photonic components and devices and spectrometers most used in optical and photonic investigation techniques in the biomedical field, in cultural heritage, in image analysis, in industrial processes, in photovoltaics and in the chemical-physical analysis, will be discussed. Practical investigation experiences in these fields will be proposed in some laboratories of the department. At the end of the course, students will develop reasoning skills and quantitative resolution abilities useful for understanding and applying the optical and photonic techniques most used in the various fields of applied physics.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) Know the fundamentals of different photonic and optical techniques and their use in the various fields of applied physics;
OF 2) Understand the principles of interaction between radiation and matter and the use of specific electromagnetic sources;
OF 3) Understand the functioning of various photonic devices, various spectrometers and various spectroscopy and microscopy techniques;

B - Application skills
OF 4) Learn to choose the most advantageous photonic and/or optical technique for specific applications;
OF 5) Understand the complementarity between the various optical and photonic techniques;
OF 6) Be able to understand the potential and experimental limitations of the various techniques considered;

C - Autonomy of judgment
OF 7) Be able to integrate the knowledge acquired in order to apply it subsequently in the more general context of applied physics;

D – Communication skills
OF 8) Know how to communicate the basic concepts of the different photonic and optical techniques and the results potentially obtainable in the various fields;

E - Learning ability
OF 9) Have the ability to independently consult basic texts and scientific articles in order to independently study some topics introduced during the course.

Educational objectives

GENERAL OBJECTIVES:
The course of Computational Statistical Mechanics aims to provide the necessary knowledge to understand and implement classical molecular dynamics and Monte Carlo techniques. The methods, that allow us to generate trajectories in phase space for sampling distinct statistical ensembles, will be studied. Some techniques which offer the possibility to calculate the free energy will be also discussed and it will be shown how the use of such results can provide a description of the atoms and molecules phase diagrams. At the end of the course, students will develop the ability of a quantitative reasoning and numerical skills useful for studying, modeling and understanding a large class of atomic and molecular systems as well as supramolecular aggregates. In addition, the student will be able to utilize the most common simulation packages which are available for a numerical study of complex systems, such as colloidal and bio-molecular systems, due to the acquired full knowledge of algorithms and numerical techniques on which these programs are built. Particular emphasis will be given to object-oriented and generic programming in the implementation of a computer simulation code. In particular, the modern C++ programming language will be introduced and discussed in the context of atomistic simulations. It will be also illustrated the use of the Python language, through the NumPy and MatPlotLib libraries, to analyze and visualize the data produced by computer simulations. During the course there will be also hands-on lectures, so that students will be able to put into practice the acquired knowledge through the implementation of their own simulation code. Students will be also stimulated to present the results obtained from the simulations, so as to test their ability to communicate clearly and effectively such results. The development of a numerical simulation code will be an opportunity for the students to design and develop their own project. This way they will be able to show their learning level and ability to apply independently the theoretical concepts acquired in the course.

SPECIFIC OBJECTIVES:

A - Knowledge and understanding
OF 1) Know common techniques to carry out computer simulations
OF 2) Know object oriented programming for scientific computations.
OF 3) Know common methods for analyzing data obtained from computer simulations.
OF 4) Understand data produced by computer simulations.

B - Application skills
OF 5) Ability to implement a simulation code.
OF 6) Ability to exploit simulations to obtain information about the physical properties of investigated systems.
OF 7) Be able to develop computer codes for analyzing data produced by computer simulations.

C - Autonomy of judgment
OF 8) Be able to critically analyze the results of “numerical experiments”.
OF 9) Be able to integrate autonomously the acquired knowledge in order to face new problems that require additional numeric techniques.
OF 10) Be able to identify the best technique to solve and study a physical problem numerically.

D - Communication skills
OF 11) Know how to communicate clearly to specialists and non-specialists, through manuscripts and presentations, the results obtained.
OF 12) Know how to clearly discuss a scientific topic.
OF 13) Know how to reproduce calculations related to a given scientific topic in a critical and informed manner.
E - Ability to learn
OF 14) Have the ability to learn new algorithms and numerical techniques by exploiting the scientific literature.
OF 15) Be able to conceive and develop their own project consisting of writing a simulation code or implementing a numerical technique.
OF 16) Be able to overcome difficulties and setbacks in the implementation of numerical techniques through original ideas and solutions.

Educational objectives

GENERAL OBJECTIVES: The "Soft and Biological Matter" course aims to provide the necessary knowledge to understand the structure of soft and biological matter, in the relevant scales of
length and time. Important arguments include the origins of the effective forces between macromolecules, the aggregation processes which result in the formation of vesicles, micelles, membranes, the formation of gel phases, structural and dynamic properties of synthetic and biological (nucleic acids and proteins) polymers. At the end of the course, students will develop quantitative reasoning and analytical skills useful for studying, modelling and understanding phenomena related to the dynamic and structural properties of soft and biological matter.
SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) To understand the physics of soft and biological matter
OF 2) To understand energetic and entropic forces
OF 3) To understand molecular aggregation
OF 4) To understand thermodynamic stability and critical phenomena in soft matter
B - Application skills
OF5) To be able to apply learned methods/techniques to novel problems
C - Autonomy of judgment
OF 6) To be able to apply the topic discussed in the course to the general context of soft and biological matter.
D - Communication skills
E - Ability to learn
OF 7) To be able to understand a scientific publication and deepen her/his own understanding of the arguments discussed in the course.

Educational objectives

A - Knowledge and understanding
OF 1) To possess a basic knowledge of complexity science, i.e. the collective properties that emerge with a large number of interacting components (atoms, particles or bacteria in a physical or biological context, or people, machines or businesses in a socio-economic context).
OF 2) Understanding the mechanisms underlying the emergence of complex macroscopic properties from knowledge of microscopic mechanisms.
OF 3) Mastering the basic toolbox of a complexity scientist: information theory, network theory, scale invariance and critical phenomena, properties of dynamical systems, agent models.
B - Application skills
OF 4) Knowing how to devise simple models for complex phenomenologies.
OF 5) Being able to tackle complex problems analytically or computationally, translating research questions into concrete solution and verification actions.
OF 6) Being able to apply the techniques and methods learnt also outside the areas covered in the course.
OF 7) Integrating the knowledge acquired in order to formalise problems and obtain results and predictions of increasing accuracy.
C - Autonomy of judgment
OF 8) Being able to analyse phenomena, also through the acquisition of data and evidence, that fall within the scope of complexity and identify their essential elements.
OF 9) Being able to synthesise phenomenologies in order to be able to distill relevant and relevant questions.
OF 10) Being able to identify interesting new research directions.
D - Communication skills
OF 11) Being able to communicate complex issues in a simple way, focusing on the essential elements and revealing cause-effect relationships as far as possible.
OF 12) Being able to organise a coherent, profound yet comprehensible presentation.
OF 13) Knowing how to express one's thoughts in a way that stimulates group work and interaction with colleagues.
E - Ability to learn
OF 14) Have the ability to consult reference texts and articles.
OF 15) Being able to assess the relevance of results, their place in the scientific panorama of reference and their potential importance for the research topics of interest.
OF 16) Being able to design and develop a research project, identifying the main objectives and the possible paths to reach them.

Educational objectives

GENERAL OBJECTIVES:
The course of Computational Statistical Mechanics aims to provide the necessary knowledge to understand and implement classical molecular dynamics and Monte Carlo techniques. The methods, that allow us to generate trajectories in phase space for sampling distinct statistical ensembles, will be studied. Some techniques which offer the possibility to calculate the free energy will be also discussed and it will be shown how the use of such results can provide a description of the atoms and molecules phase diagrams. At the end of the course, students will develop the ability of a quantitative reasoning and numerical skills useful for studying, modeling and understanding a large class of atomic and molecular systems as well as supramolecular aggregates. In addition, the student will be able to utilize the most common simulation packages which are available for a numerical study of complex systems, such as colloidal and bio-molecular systems, due to the acquired full knowledge of algorithms and numerical techniques on which these programs are built. Particular emphasis will be given to object-oriented and generic programming in the implementation of a computer simulation code. In particular, the modern C++ programming language will be introduced and discussed in the context of atomistic simulations. It will be also illustrated the use of the Python language, through the NumPy and MatPlotLib libraries, to analyze and visualize the data produced by computer simulations. During the course there will be also hands-on lectures, so that students will be able to put into practice the acquired knowledge through the implementation of their own simulation code. Students will be also stimulated to present the results obtained from the simulations, so as to test their ability to communicate clearly and effectively such results. The development of a numerical simulation code will be an opportunity for the students to design and develop their own project. This way they will be able to show their learning level and ability to apply independently the theoretical concepts acquired in the course.

SPECIFIC OBJECTIVES:

A - Knowledge and understanding
OF 1) Know common techniques to carry out computer simulations
OF 2) Know object oriented programming for scientific computations.
OF 3) Know common methods for analyzing data obtained from computer simulations.
OF 4) Understand data produced by computer simulations.

B - Application skills
OF 5) Ability to implement a simulation code.
OF 6) Ability to exploit simulations to obtain information about the physical properties of investigated systems.
OF 7) Be able to develop computer codes for analyzing data produced by computer simulations.

C - Autonomy of judgment
OF 8) Be able to critically analyze the results of “numerical experiments”.
OF 9) Be able to integrate autonomously the acquired knowledge in order to face new problems that require additional numeric techniques.
OF 10) Be able to identify the best technique to solve and study a physical problem numerically.

D - Communication skills
OF 11) Know how to communicate clearly to specialists and non-specialists, through manuscripts and presentations, the results obtained.
OF 12) Know how to clearly discuss a scientific topic.
OF 13) Know how to reproduce calculations related to a given scientific topic in a critical and informed manner.
E - Ability to learn
OF 14) Have the ability to learn new algorithms and numerical techniques by exploiting the scientific literature.
OF 15) Be able to conceive and develop their own project consisting of writing a simulation code or implementing a numerical technique.
OF 16) Be able to overcome difficulties and setbacks in the implementation of numerical techniques through original ideas and solutions.

Educational objectives

GENERAL OBJECTIVES:
The aim of the course 'Computational Solid State Physics' is to provide both theoretical and practical understanding with the two main numerical approaches currently in use for the solution of the quantum many body problem in condensed matter physics:

a) Density Functional Theory, which allows to obtain predictions from first principles of electronic states, structural energies, and interatomic forces in molecules and solids;
b) Quantum Monte Carlo methods - variational, diffusion, path-integral – which can be applied to the numerical study of various many-body quantum systems (liquid or solid helium, electron gas, electrons in atoms and molecules).

SPECIFIC OBJECTIVES:
A- Knowledge and Understanding:
OF1: To know and understand the fundamentals of Hartree-Fock (H-F) theory.
OF2: To know and understand the fundamentals of Density Functional Theory (DFT).
OF3: To know and understand the fundamentals of Pseudopotential theory (PPT).
OF4: To know and understand the DFT+PPT theory of crystalline systems.
OF5: To know and understand the variational Monte Carlo (MC) method for identical particles.
OF6: To know and understand the "projection MC" method for identical particles.
OF7: To know and understand the path integral Monte Carlo (PIMC) method.
OF8: To know and understand the "sign problem" for systems of many identical fermions.
B- Application Skills:
OF9: To apply DFT+PPT to simple solid-state systems (using software like Quantum Espresso).
OF10: To apply various quantum Monte Carlo methods to simple systems of many identical bosons or fermions (writing simple C codes and using large pre-existing FORTRAN codes).
C- Autonomy of Judgement:
OF11: To be able to assess, for a real quantum solid or fluid, which theories and algorithms presented in the course are suitable for describing and/or predicting which physical properties.
OF12: To be able to evaluate the feasibility, in terms of memory and CPU time, of a numerical project in molecular or solid-state physics.
D- Communication Skills:
OF13: To be able to present the results of a theoretical-numerical project.
OF14: To be able to write concise reports on the results of a theoretical-numerical project.
Ability to Learn:
OF15: To progress autonomously in C programming skills.
OF16: To progress autonomously in the use of existing software and codes.
OF17: To progress in graphical visualization skills of one's own results.
OF18: To progress in the ability to read reviews and research articles.

Educational objectives

GENERAL OBJECTIVES:
This course is designed as an introduction to computational biology and biophysics. It aims to bridge the gap between institutional learning and active research. The course is structured around three main aspects: i) TOPICS (principles, ideas); ii) METHODS (algorithms and computational techniques); iii) PERSPECTIVES of contemporary computational biology. Extensive reference and critical introductions to literature and current texts will be provided as guides for individual study. Efforts will be made to provide a clear framework of bibliographic references for each topic discussed, aiding in preparation for the final exam. At the end of the course, special guests will present original research lines of interest to students in biosystems, materials physics, and theoretical courses. By successfully completing the course, students will be able to navigate the world of computational biophysics at various scales (from molecules to cells) and master the main computation and analysis algorithms used in the field.

SPECIFIC OBJECTIVES:
A - Knowledge and Understanding
SO 1) Gain a historical-critical perspective of modern computational biology/biophysics
SO 2) Understand the fundamentals of modern evolutionary theory
SO 3) Gain practical experience with data analysis models based on Bayesian inference
SO 4) Gain direct experience with major bioinformatics databases (SwissProt, pFam, PDB,…)

B - Applied Skills
SO 7) Translate at least the main computational biophysics simulation and analysis algorithms into pseudo-code
SO 8) Improve programming skills in scripting languages (Python) or compiled languages (C/C++)
SO 9) Execute a molecular dynamics simulation of a small protein on GROMACS

C - Judgment Autonomy
SO 10) Evaluate the quality of a scientific article

D - Communication Skills
SO 11) Report the results of a research project to the class participants
SO 12) Actively participate in classroom discussions (in Italian and/or English)

E - Learning Skills
SO 13) Acquire fluency in consulting specific databases (e.g., PubMed, Google Scholar) to support/refute a research hypothesis
SO 14) Actively participate in the organization of self-learning groups

Educational objectives

GENERAL OBJECTIVES:
The main objective of Advanced Mathematical Methods for Physics is that of providing an introduction to up-to-date computational methods that are used in research areas of current interest. Three different courses are offered.

The goal of the third course is to provide the students with the theoretical background of perturbative and asymptotic analysis used in many fields of theoretical physics:
a) Definition and properties of the perturbative and asymptotic exapansions used in theoretical physics;
b) Introduction to some asymptiotic methods --- Boundary Layers, WKB, Multiple Scale, Renormalization Group --- and analisys of their filds of applicability.
SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) To know and understand the foundations of the perturbative methods
OF 2) To know and understand the foundations asymptotic analysis
OF 3) To know and understand the Boundary Layer Theory
OF 4) To know and understand the WKB method
OF 5) To know and understand the Multiple Scale method
OF 6) To know and understand the Renormalization Group and it connections with asymptotica analysis.

B - Application skills
OF 7) Application of the asymptotic analysis to the solution of comlex problems
OF 8) Application of the Boundary Layer Theory, WKB method and Multiple Scale method to the study of simple problems.
OF 9) Application of the Renormalization Group method to the asymptotic analysis of the solution of simple ordinary differential equations.

C - Autonomy of judgment
OF 10) Ability to analize a simple perturbative problem.
OF 11) Ability to evaluate the structure of a simple perturbative problem and use the more appropriate method to its study.
D - Communication skills
OF 12) Ability to create an effective presentation of the results of a theoretical project
OF 13) Ability to present the basis of the asymptotic analysis and some of its methods.
E - Ability to learn
OF 14) Autonomous improvement in the study of perturbation method
OF 15) Autonomous improvement in the use of asymptotic analysis in more comlex problems
OF 16) Autonomous improvement in reading and understanding research articles and reviews

Educational objectives

GENERAL OBJECTIVES:
The course aims to introduce students to the fundamental concepts of statistical inference and its applications in modern biology, utilizing the language and methods of statistical physics and complexity science. By the end of the course, students should be able to master the theoretical concepts of information and entropy, and to apply analytical and computational approaches (via Python/Google Colab notebooks) to solve real-world problems related to the analysis of high-dimensional biological and biophysical data.

SPECIFIC OBJECTIVES:
A – Knowledge and Understanding
OF 1) To acquire knowledge of the fundamentals of Bayesian inference and asymptotic inference, and their deep connection to the principle of maximum entropy and statistical physics.
OF 2) To understand key concepts in information theory (Shannon entropy, mutual information, Fisher-Shannon information) and the mechanisms of phase transitions in high-dimensional inference.
OF 3) To develop the ability to comprehend the mathematical structure of statistical physics models and unsupervised/supervised learning models applied to biological systems (Boltzmann Machines, Ising Models, Hidden Markov Models – HMMs, and simple neural networks).
B – Applied Skills
OF 4) To be able to estimate physical and biological parameters (e.g., diffusion coefficients) based on sparse experimental data or single-particle tracking data.
OF 5) To be able to apply dimensionality reduction techniques (PCA and Sparse PCA) to identify structured patterns within complex biological data, such as the activity of neural populations.
OF 6) To be able to implement regularization strategies—including the use of priors and sparsity constraints—to prevent overfitting in the data-scarce regimes typical of biological research.
OF 7) To be able to utilize network inference and maximum entropy methods (Direct Coupling Analysis) to predict structural contacts in proteins, model molecular evolution, and generate artificial sequences.
OF 8) To be able to analyze time series and genomic data using Markov chains and Hidden Markov Models (HMMs) to study signal propagation and the organization of viral genomes.
C – Independent Judgment
OF 9) To be able to critically evaluate which statistical model or computational architecture is most suitable for describing a biological dataset, balancing model complexity against the quantity of available data (data-scarce regime).
OF 10) To be able to integrate methodologies from the statistical physics of disordered systems and information theory to interpret phenomena of emergent behavior and collective organization in living systems.
D – Communication Skills
OF 11) Be able to present the results of biophysical data analysis clearly, rigorously, and using appropriate interdisciplinary formalism, translating physical concepts (e.g., temperature, free energy) into biological or information-theoretic properties, and vice versa.
E – Learning Skills
OF 12) Possess the ability to independently consult advanced scientific textbooks, research monographs, and literature articles in the fields of applied statistical physics, quantitative biology, and physics-based machine learning.

Educational objectives

GENERAL OBJECTIVES: The "Soft and Biological Matter" course aims to provide the necessary knowledge to understand the structure of soft and biological matter, in the relevant scales of
length and time. Important arguments include the origins of the effective forces between macromolecules, the aggregation processes which result in the formation of vesicles, micelles, membranes, the formation of gel phases, structural and dynamic properties of synthetic and biological (nucleic acids and proteins) polymers. At the end of the course, students will develop quantitative reasoning and analytical skills useful for studying, modelling and understanding phenomena related to the dynamic and structural properties of soft and biological matter.
SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) To understand the physics of soft and biological matter
OF 2) To understand energetic and entropic forces
OF 3) To understand molecular aggregation
OF 4) To understand thermodynamic stability and critical phenomena in soft matter
B - Application skills
OF5) To be able to apply learned methods/techniques to novel problems
C - Autonomy of judgment
OF 6) To be able to apply the topic discussed in the course to the general context of soft and biological matter.
D - Communication skills
E - Ability to learn
OF 7) To be able to understand a scientific publication and deepen her/his own understanding of the arguments discussed in the course.

Educational objectives

GENERAL OBJECTIVES:

The main goal of the course is to introduce students to the mathematical theory of groups (mainly: discrete groups and compact Lie groups) by a Mathematical Physics approach which emphasizes the role of representations of symmetries in terms of states or observables of the corresponding theory. Such an approach allows an immediate comparison between classical theories (Poisson brackets) and quantum theories (commutators).

SPECIFIC OBJECTIVES:

A - Knowledge and understanding
OF1) To know the fundamental concepts in the theory of finite groups and matrix Lie groups, and in the theory of their linear, unitary or projective representations.
OF2) To know the mathematical structure of the Lie groups which more often appear in physical theories, and to understand the relation between such groups and the symmetries of the physical theory.
OF3) To understand the role of symmetries and Lie groups in (relativistic) field theories.
OF4) To understand the mathematical language of differential forms, and the reformulation of electromagnetism in such a language.

B – Application skills
OF 5) To be able to compute the commutation relations among the generators of the Lie algebra of a given (matrix) Lie group; to be able to explicitly compute such commutation relations in the most relevant cases: the rotation group, the Poincaré group, and the group SU(3).
OF 6) To be able to compute the tensor product of two representations of the rotation group, by using the Wigner Eckart theorem; to be able to interpret the result of such a computation in the application to compound systems (e.g. molecules).
OF7) To be able to determine whether a given differential form is closed and/or exact; to be able to translate the concepts concerning differential forms in the analogous concepts of vector analysis (gradient, curl or rotational, divergence) and vice versa.

C - Autonomy of judgment
OF 8) To be able to critically read an advanced book on symmetries in physics.
OF 9) To be able to integrate the knowledge acquired within the course, in order to apply them in the context of different physical theories, in connection e.g. with high energy physics or with condensed matter physics.

D – Communication skills
OF 10) Ability to discuss the symmetries of a physical system by appropriately using the language of differential forms and Lie groups.

E - Ability to learn
OF 11) Ability to read advanced monographies and research papers, which usually use the mathematical language of Lie groups and differential forms.
OF 12) Ability to "construct" a physical theory, by implementing in the theory the symmetries of the physical system under investigation, using Lie algebras and Lie groups as a fundamental tool.

Educational objectives

GENERAL OBJECTIVES:
The main objective of the course in Theoretical Biophysics is to show how statistical physics has a crucial role for a quantitative understanding of many biological
phenomena. To this aim, the course focuses on two very general aspects present in a variety of biological processes: the role of noise and the signal to noise ratio; the
emergence of collective phenomena.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) To acquire some fundamental background in statistical physics, related in particular to elementary stochastic processes, critical phenomena and statistical inference
OF 2) To learn the phenomenology of several important biological processes such as chemotaxis and chemoreception, photoreception, proteins, neural networks, living active matter and collective motion.
OF 3) to acquire modeling techniques

B - Application skills
OF 4) To be able to apply theoretical concepts and models to the quantitative description of the phenomenology experimentally characterized. To build models starting from the data.

C - Autonomy of judgment
OF 5) To be able to modify approaches derived from statistical physics to study specific phenomena occurring in biological systems.

D - Communication skills

E - Ability to learn
OF 6) Have the ability to consult and study scientific texts and literature of both theoretical and experimental character in a highly interdisciplinary context.

Educational objectives

GENERAL OBJECTIVES:
The goal of the course is the study of the foundations of the
statistical mechanics
of non equilibrium systems, with special enphasis on stochastic
models (e.q. Langevin equations)
i) to provide the student with a deep knowledge and understanding of
these
concepts, and
ii) to allow him (her) to successfully apply them in various physical
contexts. In particular, the student must be able to
use techniques of integration in the complex domain in all the
physical contexts in which they have applications.

SPECIFIC OBJECTIVES:

A - Knowledge and understanding
- To know the basis of the kinetic theory
- To understand how to use stochastic processes

B - Application skills
- To know the theory of fluctuations and the linear response

C - Autonomy of judgment
- To be able to integrate the knowledge acquired in order to apply it in
the more general context of statistical mechanics

E - Ability to learn
- To be able to read independently scientific texts and articles in
order to elaborate on the topics introduced in the course.

Educational objectives

General Objectives:
To acquire knowledge of fundamental topics in Mathematical Physics and the related mathematical methods.

Specific Objectives:

Knowledge and Understanding:

By the end of the course, students will be familiar with the fundamentals of operator theory in Hilbert spaces, the mathematical structure of quantum mechanics, and the basic methods for studying problems in quantum mechanics from the perspective of mathematical physics.

Applying knowledge and understanding:

Students who pass the exam will be able to: i) apply the results of operator theory, ii) construct self-adjoint Hamiltonians and study their spectra, iii) rigorously approach a scattering problem, iv) understand the mathematical methods required for the study of the dynamics of many-body systems, with particular regard to the phenomenon of condensation.

Critical Thinking and Judgment:

Students who pass the exam will be able to recognize a mathematical-physical approach and analyze similarities and differences compared to the typical approach in Theoretical Physics.

Communication Skills:

Students who pass the exam will have developed the ability to communicate concepts, ideas, and methodologies in mathematical physics.

Learning Skills:

The knowledge acquired will enable students to pursue further study—either independently or through other courses—on more specialized aspects of the methods of mathematical physics.

Educational objectives

A - Knowledge and understanding
OF 1) Starting from the study of neurobiology of the nervous system, the student will first concentrate on the mechanisms regulating the electro-chemical properties of nerve cells and their connections, eventually studing the dynamics of populations of neuronal networks. The knowledge acquired will be on nonlinear and statistical physics compared to experimental data.
OF 2) The students will develop generally applicable skills in the field of theoretical physics of the complex systems and the nonlinear dynamics.
B - Application skills
OF 3) The student will be able to understand the dynamics of neuronal populations at the basis of the cognitive functions like decision making and short-term memory.
OF 4) The student will be able to apply analysis techniques and methods to electrophysiological data.
C - Autonomy of judgment
OF 5) By attending the lessons and with the regular interaction during the lessons themselves, the student will develop adequate autonomy of judgment, as he/she will be able to interface constantly with the teacher and critically analyze the information learned.
D - Communication skills
OF 6) The skills on the neurobiology of the nervous system will allow the student to interact with environments different from physics, enabling him/her to initiate multidisciplinary interactions in the life sciences.
E - Ability to learn
OF 7) The student will have the ability to evaluate and solve various problems of both data analysis and physics of complex systems.
OF 8) The acquired knowledge will allow the student to tackle the study of interdisciplinary papers on the physical phenomena underlying the behavior of the nervous system.

Educational objectives

GENERAL OBJECTIVES:
The course introduces the students to Condensed Matter phenomena related to the interaction between electrons, and of electrons with external electromagentic fields.
SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1 The Condensed Matter Physics II course provides a theoretical introduction students to the main methods and phenomena of condensed matter physics, related to electron-electron interactions.
The course will also feature selected examples of the applications of condensed matter theory methods to real-world research problems.
B - Application skills
OF 2: Theory lectures will be integrated by practical (analytical and numerical) exercises, addressing real-world problems.
C - Autonomy of judgment
OF3: After attending course, students will have developed quantitative and qualitative problem-solving skills related to condensed matter theory, which will allow them to understand and model fundamental phenomena in condensed matter.

D - Communication skills

E - Ability to learn
OF 6) To be able to read independently scientific texts and articles in order to elaborate on the topics introduced in the course.

Educational objectives

GENERAL OBJECTIVES:
The course in Physics of Liquids aims to provide the necessary knowledge
to understand the disordered state of matter. Emphasis will be directed toward the
connection between the inter-particle interaction potential and the resulting
equilibrium structure. The themes of short-range ordering
and of the dynamics in the fluid and glass phases
will be studied in depth. At the end of the course, students will develop quantitative reasoning skills and analytical abilities useful for studying, modelling and understanding phenomena related to disordered soft matter.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) To know the theory of classical fluids, from mean field models, to integral theories and perturbative approaches.
OF 2) To understand the physical basis of the integral closures.
OF 3) To know how to extract structural and dynamical quantities from the scattering of X rays and neutrons.
OF 4) Know how to go from a microscopic theory to a hydrodynamic theory.
B - Application skills
OF 5) To be able to compute the cluster integrals that compose the virial coefficient for simple interaction potentials.
OF 6) To be able to solve the equations governing the structure of a fluid in the presence of external fields.
OF 7) To be able to apply perturbative techniques
…
C - Autonomy of judgment
OF 8) To be able to understand the results of experiments and simualtions on simple and complex liquids.
OF 9) To be able to integrate the knowledge acquired in order to choose the best closure relations for a particular problem.
D - Communication skills
OF 10) To know how to communicate the results of experiments and simulations on simple liquids.

E - Ability to learn
OF 11) Have the ability to consult and understand books and articles in order to gain a deeper knowledge of the topics discussed during the course.

Educational objectives

GENERAL OBJECTIVES

The bacterial cell occupies the same special place in biological physics as the hydrogen atom does in condensed matter physics, and for the same reasons. Bacteria are the first "atoms" of life to appear in the known Universe, and everything fundamental in life is found in bacteria, in its simplest forms. The aim of the course is to investigate some fundamental aspects of living systems in a journey that starts from the internal mechanisms by which the bacterial cell "thinks" and acts, passing through how the individual cell moves in the external physical environment and ending with the study of the collective behaviour of bacterial colonies.
All topics covered in the course are based on recent literature and discuss both experimental aspects and theoretical modelling.

SPECIFIC OBJECTIVES

A - Knowledge and understanding
OF 1) To know and understand the fundamentals of gene regulation in prokaryotes and the dynamics of transcriptional networks.
OF 2) To know and understand the fundamentals of low Reynolds number fluid dynamics.
OF 3) To know and understand the main manifestations of the out of equilibrium nature of active matter.

B - Application skills
OF 4) To be able to discuss the dynamical behaviour of a transcriptional network.
OF 5) Tp be able to solve some elementary problems of low Reynolds hydrodynamics.
OF 6) Tp be able to model the stochastic dynamics of active particle systems.
OF 7) To be able to describe with continuous models the growth of bacterial colonies.

C - Autonomy of judgement
OF 8) Using the knowledge acquired, the student will be able to formulate new models capable of describing situations not covered in the course.

D - Communication skills
OF 9) To know how to communicate in written reports an advanced concept.
OF 10) To be able to present a recent line of research in biophysics.

E - Ability to learn
OF 11) To be able to read independently scientific texts and articles in order to elaborate on the topics introduced in the course.

Educational objectives

Formative targets:

The objectives of the course are to bring the student to a deep knowledge and understanding of the basic mathematical properties i) of the nonlinear wave propagation with or without dispersion or dissipation; ii) of the construction of nonlinear mathematical models of physical interest, through the multiscale method, like the soliton equations, and of the mathematical techniques to solve them, arriving to the introduction of current research topics in the theory of solitons and anomalous waves. At the end of the course the student must be able i) to apply the acquired methods to problems in nonlinear physics even different from those studied in the course, in fluid dynamics, nonlinear optics, theory of gravitation, etc .., solving typical problems of the nonlinear dynamics; ii) to integrate in autonomy the acquired knowledges through the suggested literature, to solve also problems of interest for him/her, and not investigated in the course. The student will have the ability to consult supplementary material, interesting scientific papers, having acquired the right knowledges and critical skill to evaluate their content and their potential benefits to his/her scientific interests. At last the student must be able to conceive and develop a research project in autonomy. In order to achieve these goals, we plan to involve the student, during the theoretical lectures and exercises, through general and specific questions related to the subject; or through the presentation in depth of some specific subject agreed with the teacher.

Educational objectives

GENERAL OBJECTIVES:
Acquire familiarity with advanced deep learning techniques based on differentiable neural network models with supervised, unsupervised and reinforced learning paradigms; acquire skills in modelling complex problems through deep learning techniques, and be able to apply them to different application contexts in the fields of physics and basic and applied scientific research.

Discussed topics include: general machine learning concepts, differentiable neural networks, regularization techniques. Convolutional neural network, neural network for sequence analysis (RNN, LSTM / GRU, Transformers). Advanced learning techniques: transfer learning, domain adaptation, adversarial learning, self-supervised and contrastive learning, model distillation.
Graph Neural Networks (static and dynamic) and application to structured models for physics: dynamic models, simulation of complex fluids, GNN Hamiltonians and Lagrangians. Generative and variational models: variational mean-field theory, expectation maximization, energy based and maximum entropy models (Hopfield networks, Boltzman machines and RBM), AutoEncoders, Variational AutoEncoders, GANs, Autoregressive flow models, invertible networks, generative models based on GNN. Quantum Neural Networks.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) Knowledge of the functioning of neural networks and their mathematical interpretation as universal approximators
OF 2) Understanding of the limits and potential of advanced machine learning models
OF 3) Understanding of the limits and potential of DL in solving physics problems

B - Application skills
OF 4) Design, implementation, commissioning and analysis of deep learning architectures to solve complex problems in physics and scientific research.

C - Autonomy of judgment
OF 5) To be able to evaluate the performance of different architectures, and to evaluate the generalization capacity of the same

D - Communication skills
OF 6) Being able to clearly communicate the formulation of an advanced learning problem and its implementation, its applicability in realistic contexts
OF 7) Being able to motivate and to evaluate the generalization capacity of a DL model

E - Ability to learn
OF 8) Being able to learn alternative and more complex techniques
OF 9) Being able to implement existing techniques in an efficient, robust and reliable manner

Educational objectives

A - Knowledge and understanding
OF 1) To possess a basic knowledge of complexity science, i.e. the collective properties that emerge with a large number of interacting components (atoms, particles or bacteria in a physical or biological context, or people, machines or businesses in a socio-economic context).
OF 2) Understanding the mechanisms underlying the emergence of complex macroscopic properties from knowledge of microscopic mechanisms.
OF 3) Mastering the basic toolbox of a complexity scientist: information theory, network theory, scale invariance and critical phenomena, properties of dynamical systems, agent models.
B - Application skills
OF 4) Knowing how to devise simple models for complex phenomenologies.
OF 5) Being able to tackle complex problems analytically or computationally, translating research questions into concrete solution and verification actions.
OF 6) Being able to apply the techniques and methods learnt also outside the areas covered in the course.
OF 7) Integrating the knowledge acquired in order to formalise problems and obtain results and predictions of increasing accuracy.
C - Autonomy of judgment
OF 8) Being able to analyse phenomena, also through the acquisition of data and evidence, that fall within the scope of complexity and identify their essential elements.
OF 9) Being able to synthesise phenomenologies in order to be able to distill relevant and relevant questions.
OF 10) Being able to identify interesting new research directions.
D - Communication skills
OF 11) Being able to communicate complex issues in a simple way, focusing on the essential elements and revealing cause-effect relationships as far as possible.
OF 12) Being able to organise a coherent, profound yet comprehensible presentation.
OF 13) Knowing how to express one's thoughts in a way that stimulates group work and interaction with colleagues.
E - Ability to learn
OF 14) Have the ability to consult reference texts and articles.
OF 15) Being able to assess the relevance of results, their place in the scientific panorama of reference and their potential importance for the research topics of interest.
OF 16) Being able to design and develop a research project, identifying the main objectives and the possible paths to reach them.

Educational objectives

GENERAL OBJECTIVES:
The main objective of the course in Theoretical Biophysics is to show how statistical physics has a crucial role for a quantitative understanding of many biological
phenomena. To this aim, the course focuses on two very general aspects present in a variety of biological processes: the role of noise and the signal to noise ratio; the
emergence of collective phenomena.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) To acquire some fundamental background in statistical physics, related in particular to elementary stochastic processes, critical phenomena and statistical inference
OF 2) To learn the phenomenology of several important biological processes such as chemotaxis and chemoreception, photoreception, proteins, neural networks, living active matter and collective motion.
OF 3) to acquire modeling techniques

B - Application skills
OF 4) To be able to apply theoretical concepts and models to the quantitative description of the phenomenology experimentally characterized. To build models starting from the data.

C - Autonomy of judgment
OF 5) To be able to modify approaches derived from statistical physics to study specific phenomena occurring in biological systems.

D - Communication skills

E - Ability to learn
OF 6) Have the ability to consult and study scientific texts and literature of both theoretical and experimental character in a highly interdisciplinary context.

Educational objectives

GENERAL OBJECTIVES:
The goal of the course is the study of the foundations of the
statistical mechanics
of non equilibrium systems, with special enphasis on stochastic
models (e.q. Langevin equations)
i) to provide the student with a deep knowledge and understanding of
these
concepts, and
ii) to allow him (her) to successfully apply them in various physical
contexts. In particular, the student must be able to
use techniques of integration in the complex domain in all the
physical contexts in which they have applications.

SPECIFIC OBJECTIVES:

A - Knowledge and understanding
- To know the basis of the kinetic theory
- To understand how to use stochastic processes

B - Application skills
- To know the theory of fluctuations and the linear response

C - Autonomy of judgment
- To be able to integrate the knowledge acquired in order to apply it in
the more general context of statistical mechanics

E - Ability to learn
- To be able to read independently scientific texts and articles in
order to elaborate on the topics introduced in the course.

Educational objectives

GENERAL OBJECTIVES:
The main objective of the course is to illustrate the characteristics of some of the best known disordered models and to introduce the approximations and analytical techniques that allow their study in statistical mechanics.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) To know the main disordered models, such as dilute ferromagnets, ferromagnets with random external field, and spin glasses
OF 2) To understand the different physical behaviors that arise as a result of the introduction of quenched disorder (slowing down of the dynamics, metastability, presence of many thermodynamic states).
OF 3) To know the main techniques of statistical mechanics (mean-field approximations, replica and cavity methods) that allow the analytical study of models with disorder.

B - Application skills
OF 4) To know how to apply an analytical technique (mean-field approximation, replica and cavity method) to a given Hamiltonian to study its physical behavior.
C - Autonomy of judgment
OF 5) Be able to recognize to which class of disordered systems a given Hamiltonian belongs.

D - Communication skills
OF 6) Ability to present the course topics orally in a non-technical language that allows understanding even by those who have not yet taken the course.
E - Ability to learn
OF 7) To be able to read scientific texts and articles in order to independently investigate the topics introduced during the course.

Educational objectives

GENERAL OBJECTIVES:
The course is an advanced module aimed at guiding the students through a journey at the boundary between statistical physics and machine learning by introducing advanced concepts of equilibrium and out of equilibrium statistical mechanics and by illustrating their applications to learning models and development of artificial intelligence.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) To acquire the main methods of statistical mechanics, probability and information theory relevant to applications in machine learning and inference, such as the replica approach, message passing, mutual information, data compression, Bayesian approaches
OF 2) To understand the different physical behaviour shown by inference and artificial learning procedures (curse of dimensionality, metastability, presence of multiple thermodynamic states)
B - Application skills
OF 3) To know how to apply an analytical technique to a given inference or learning setting to study its physical behavior
C - Autonomy of judgment
OF 4) Be able to recognize to which class of disordered systems a given inference or learning setting belongs
D - Communication skills
OF 5) Ability to learn from oral presentation of research results on topics similar to those introduced during the course
OF 6) Ability to present the course topics orally in a non-technical language that allows understanding even by those who have not yet taken the course
E - Ability to learn
OF 7) To be able to read scientific texts and articles in order to independently investigate the topics introduced during the course

Educational objectives

GENERAL OBJECTIVES:

The course provides an introduction to the mathematical physics approach to
Statistical Field Theory, based in particular on bosonic and fermionic functional integrals, the theory of Renormalization
and the Wilsonian Renormalization Group. Such tools provide an unifying conceptual framework and a common language for several physical problems, charapterized by infinitely many interacting degrees of freedom and ranging from quantum or classical statistical physics to high energy physics. Solvable models will be also treated via exact methods, like bosonization or fermionization.

We will focus in particular: on phase transitions, universality and critical behavior in statistical mechanics models like Ising o Phi4; on the ultraviolet high energy problem posed by
Euclidean Quantum Field Theory models and their non perturbative construction with finite or infinite lattice cut-off, including the role of Ward Identities and chiral anomalies; on condensed matter systems with an emerging field theory description, and in particular on the universality of transport coefficients in graphene or topological insulators.

SPECIFIC OBJECTIVES:

A - Knowledge and understanding

1)To know and understand the rigorous results on
Phase transition, universality and critical phenomena in systems like the Ising, phi4 or dimer models, in solvable or non solvable cases and in cases with gaussian or non trivial fixed points.

2)To know and understand the constructive Euclidean approach to Quantum Field Theory, including the theory of renormalization, the non-perturbative construction of low dimensional models like Thirring or Gross Neveu models and the infrared limit in higher dimensions, the mathematical theory of chiral anomalies and their non-renormalization.

3)To know and understand the theory of universality of transport cofficients in condensed matter systems like Graphene, Luttinger liquids or topological insulators in presence of weak interactions.

B – Application skills

4) To be able to prove rigorous mathematical physics results
like the existence of the thermodynamic limit or to exacty compute physical observables in solvable models like 2d Ising or dimer models.

5)To be able to apply rigorous Renormalization Group methods to physical systems, writing observables in terms of expansions in the running coupling constants, to prove the renormalizability at any order and derive order by order bounds, and when possible
To extract non-perturbative informations in suitable regions of the parameters.

6) To be able to implement cancellations due to exact or emerging symmetries, to control the irrelevant terms, to derive Ward Identities and the beta function equations.

C - Autonomy of judgment

7) To be able to distinguish in the literature between conjectures, approximations and rigorous statements.

D –Communication skilll

8) Ability to explain, using the unifying language provided by the Renormalization Group ,different physical phenomana, showing the connections provided by the universal underlying structure.

E - Ability to learn

9) Ability of Critical reading, understanding and reproducing results in the modern mathematical and theoretical physics literature.

10)Use of rigorous methods to prove established but open conjectures.

11) Ability to apply the mathematical physics tools to interesting and open physical problems requiring advanced mathematics.

Educational objectives

A - Knowledge and understanding
OF 1) To possess a basic knowledge of complexity science, i.e. the collective properties that emerge with a large number of interacting components (atoms, particles or bacteria in a physical or biological context, or people, machines or businesses in a socio-economic context).
OF 2) Understanding the mechanisms underlying the emergence of complex macroscopic properties from knowledge of microscopic mechanisms.
OF 3) Mastering the basic toolbox of a complexity scientist: information theory, network theory, scale invariance and critical phenomena, properties of dynamical systems, agent models.
B - Application skills
OF 4) Knowing how to devise simple models for complex phenomenologies.
OF 5) Being able to tackle complex problems analytically or computationally, translating research questions into concrete solution and verification actions.
OF 6) Being able to apply the techniques and methods learnt also outside the areas covered in the course.
OF 7) Integrating the knowledge acquired in order to formalise problems and obtain results and predictions of increasing accuracy.
C - Autonomy of judgment
OF 8) Being able to analyse phenomena, also through the acquisition of data and evidence, that fall within the scope of complexity and identify their essential elements.
OF 9) Being able to synthesise phenomenologies in order to be able to distill relevant and relevant questions.
OF 10) Being able to identify interesting new research directions.
D - Communication skills
OF 11) Being able to communicate complex issues in a simple way, focusing on the essential elements and revealing cause-effect relationships as far as possible.
OF 12) Being able to organise a coherent, profound yet comprehensible presentation.
OF 13) Knowing how to express one's thoughts in a way that stimulates group work and interaction with colleagues.
E - Ability to learn
OF 14) Have the ability to consult reference texts and articles.
OF 15) Being able to assess the relevance of results, their place in the scientific panorama of reference and their potential importance for the research topics of interest.
OF 16) Being able to design and develop a research project, identifying the main objectives and the possible paths to reach them.

Educational objectives

A - Knowledge and understanding
OF 1) To possess a basic knowledge of complexity science, i.e. the collective properties that emerge with a large number of interacting components (atoms, particles or bacteria in a physical or biological context, or people, machines or businesses in a socio-economic context).
OF 2) Understanding the mechanisms underlying the emergence of complex macroscopic properties from knowledge of microscopic mechanisms.
OF 3) Mastering the basic toolbox of a complexity scientist: information theory, network theory, scale invariance and critical phenomena, properties of dynamical systems, agent models.
B - Application skills
OF 4) Knowing how to devise simple models for complex phenomenologies.
OF 5) Being able to tackle complex problems analytically or computationally, translating research questions into concrete solution and verification actions.
OF 6) Being able to apply the techniques and methods learnt also outside the areas covered in the course.
OF 7) Integrating the knowledge acquired in order to formalise problems and obtain results and predictions of increasing accuracy.
C - Autonomy of judgment
OF 8) Being able to analyse phenomena, also through the acquisition of data and evidence, that fall within the scope of complexity and identify their essential elements.
OF 9) Being able to synthesise phenomenologies in order to be able to distill relevant and relevant questions.
OF 10) Being able to identify interesting new research directions.
D - Communication skills
OF 11) Being able to communicate complex issues in a simple way, focusing on the essential elements and revealing cause-effect relationships as far as possible.
OF 12) Being able to organise a coherent, profound yet comprehensible presentation.
OF 13) Knowing how to express one's thoughts in a way that stimulates group work and interaction with colleagues.
E - Ability to learn
OF 14) Have the ability to consult reference texts and articles.
OF 15) Being able to assess the relevance of results, their place in the scientific panorama of reference and their potential importance for the research topics of interest.
OF 16) Being able to design and develop a research project, identifying the main objectives and the possible paths to reach them.

Educational objectives

A - Knowledge and understanding
OF 1) To know the fundamentals of the theory of stochastic processes, discrete and continuous, and thier formal framework in terms of resolution of Chapman-Kolmogorov, Fokker-Planck and master equations.
OF 2) To understand the similarities with the properties of equations already known to the students (like Schroedinger equation) and to learn equation resolution methods using operational calculus.
OF 3) To know the formalism of stochastic integration of stochastic differential equations and the connection to the Fokker-Planck partial differential equation.
B - Application skills
OF 4) To deduce physical properties of systems from the analysis of the stochastic equations.
OF 5) To apply newly learned methods to the estimate of first passage times and to the consequences of Arrhenius law on relaxation towards equilibrium in systems with rough potential landscapes.
OF 6) To apply methods and techniques to systems of different nature at and off equilibrium (viscous liquids, wave systmes, glassy systems, lasers).
C - Autonomy of judgment
OF 7) To be able to integrate acquired knwoledge and apply it also to cases not explicitly treated in the course.
OF 8) To be able to connect acquired knowledge to previous one, formalizing known concepts and connetcing them to more complex cases.
D - Communication skills
OF 9) To know how to orally present a demonstration procedure or an application assessing the most relevant and clarifying steps and their meaning.
E - Ability to learn
OF 10) To be able to consult diferrent textbooks and scientifc papers to the aim of autonomously deepening some of the arguments covered by the course.
OF 11) To be able to evaluate the effectiveness of the various studied approaches in relation to the treated problems.

Educational objectives

GENERAL OBJECTIVES:
The main objective of the course is to illustrate the characteristics of some of the best known disordered models and to introduce the approximations and analytical techniques that allow their study in statistical mechanics.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) To know the main disordered models, such as dilute ferromagnets, ferromagnets with random external field, and spin glasses
OF 2) To understand the different physical behaviors that arise as a result of the introduction of quenched disorder (slowing down of the dynamics, metastability, presence of many thermodynamic states).
OF 3) To know the main techniques of statistical mechanics (mean-field approximations, replica and cavity methods) that allow the analytical study of models with disorder.

B - Application skills
OF 4) To know how to apply an analytical technique (mean-field approximation, replica and cavity method) to a given Hamiltonian to study its physical behavior.
C - Autonomy of judgment
OF 5) Be able to recognize to which class of disordered systems a given Hamiltonian belongs.

D - Communication skills
OF 6) Ability to present the course topics orally in a non-technical language that allows understanding even by those who have not yet taken the course.
E - Ability to learn
OF 7) To be able to read scientific texts and articles in order to independently investigate the topics introduced during the course.

Educational objectives

GENERAL OBJECTIVES:
The course is an advanced module aimed at guiding the students through a journey at the boundary between statistical physics and machine learning by introducing advanced concepts of equilibrium and out of equilibrium statistical mechanics and by illustrating their applications to learning models and development of artificial intelligence.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) To acquire the main methods of statistical mechanics, probability and information theory relevant to applications in machine learning and inference, such as the replica approach, message passing, mutual information, data compression, Bayesian approaches
OF 2) To understand the different physical behaviour shown by inference and artificial learning procedures (curse of dimensionality, metastability, presence of multiple thermodynamic states)
B - Application skills
OF 3) To know how to apply an analytical technique to a given inference or learning setting to study its physical behavior
C - Autonomy of judgment
OF 4) Be able to recognize to which class of disordered systems a given inference or learning setting belongs
D - Communication skills
OF 5) Ability to learn from oral presentation of research results on topics similar to those introduced during the course
OF 6) Ability to present the course topics orally in a non-technical language that allows understanding even by those who have not yet taken the course
E - Ability to learn
OF 7) To be able to read scientific texts and articles in order to independently investigate the topics introduced during the course

Educational objectives

GENERAL OBJECTIVES:

The course provides an introduction to the mathematical physics approach to
Statistical Field Theory, based in particular on bosonic and fermionic functional integrals, the theory of Renormalization
and the Wilsonian Renormalization Group. Such tools provide an unifying conceptual framework and a common language for several physical problems, charapterized by infinitely many interacting degrees of freedom and ranging from quantum or classical statistical physics to high energy physics. Solvable models will be also treated via exact methods, like bosonization or fermionization.

We will focus in particular: on phase transitions, universality and critical behavior in statistical mechanics models like Ising o Phi4; on the ultraviolet high energy problem posed by
Euclidean Quantum Field Theory models and their non perturbative construction with finite or infinite lattice cut-off, including the role of Ward Identities and chiral anomalies; on condensed matter systems with an emerging field theory description, and in particular on the universality of transport coefficients in graphene or topological insulators.

SPECIFIC OBJECTIVES:

A - Knowledge and understanding

1)To know and understand the rigorous results on
Phase transition, universality and critical phenomena in systems like the Ising, phi4 or dimer models, in solvable or non solvable cases and in cases with gaussian or non trivial fixed points.

2)To know and understand the constructive Euclidean approach to Quantum Field Theory, including the theory of renormalization, the non-perturbative construction of low dimensional models like Thirring or Gross Neveu models and the infrared limit in higher dimensions, the mathematical theory of chiral anomalies and their non-renormalization.

3)To know and understand the theory of universality of transport cofficients in condensed matter systems like Graphene, Luttinger liquids or topological insulators in presence of weak interactions.

B – Application skills

4) To be able to prove rigorous mathematical physics results
like the existence of the thermodynamic limit or to exacty compute physical observables in solvable models like 2d Ising or dimer models.

5)To be able to apply rigorous Renormalization Group methods to physical systems, writing observables in terms of expansions in the running coupling constants, to prove the renormalizability at any order and derive order by order bounds, and when possible
To extract non-perturbative informations in suitable regions of the parameters.

6) To be able to implement cancellations due to exact or emerging symmetries, to control the irrelevant terms, to derive Ward Identities and the beta function equations.

C - Autonomy of judgment

7) To be able to distinguish in the literature between conjectures, approximations and rigorous statements.

D –Communication skilll

8) Ability to explain, using the unifying language provided by the Renormalization Group ,different physical phenomana, showing the connections provided by the universal underlying structure.

E - Ability to learn

9) Ability of Critical reading, understanding and reproducing results in the modern mathematical and theoretical physics literature.

10)Use of rigorous methods to prove established but open conjectures.

11) Ability to apply the mathematical physics tools to interesting and open physical problems requiring advanced mathematics.

Educational objectives

General objectives

Acquiring basic knowledge on the mathematical methods used in artificial intelligence modeling, with particular attention to "machine learning".

Specific objectives

Knowledge and understanding: at the end of the course the student will have knowledge of the basic notions and results (mainly in the areas of stochastic processes and statistical mechanics) used in the study of the main models of neural networks (e.g., Hopfield networks, Boltzmann machines, feed-forward networks).

Apply knowledge and understanding: the student will be able to identify the optimal architecture for a certain task and to solve the resulting model by determining a phase diagram; the student will have the basis to independently develop algorithms for learning and retrieval.

Critical and judgmental skills: the student will be able to determine the parameters that control the qualitative behaviour of a neural network and to estimate the values of these parameters that allow a good performance of the network; she/he will also be able to investigate the analogies and relationships between the topics covered during the course and during courses dedicated to statistics and data analysis.

Communication skills: ability to expose the contents in the oral and written part of the verification, possibly by means of presentations.

Learning skills: the knowledge acquired will allow a study, individual or taught in a LM course, related to more specialised aspects of statistical mechanics, development of algorithms, usage of big data.

Educational objectives

GENERAL OBJECTIVES:
The course aims to introduce the foundations of Superconductivity and Superfluidity. A preliminary part will be devoted to the phenomenological London and Ginzburg-Landau theories. The latter will be used to introduce the more general topic of spontaneous symmetry breaking in second-order phase transition, and the Anderson-Higgs mechanism for superconductivity. After discussion of the second-quantization for many-body fermionic and bosonic systems the focus will be on the microscopic models for superconductors (BCS Bardeen_Cooper e Schrieffer theory) and superfluids.
The final part will consist in a brief overview of current research topics on unconventional superconductors.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) To know the basis of the superconducting phenomenon, its phenomenological and microscopic description and its experimental applications
OF 2) To understand key concepts as spontaneous symmetry breaking and order parametr for a phase transition, with particular emphasis on continous symmetries.
OF 3) To know basic applications of second quantization to fermionic and bosonic many-particle systems
B - Application skills
OF 4) To be able to describe the superfluid phenomen both for fermions and bosons, and its theoretical and experimental implications
C - Autonomy of judgment
OF 5) To be able to integrate the knowledge acquired in order to apply in the more general context of unconventional superconduvtivity and interacting fermionic systems
E - Ability to learn
OF 6) Have the ability to read scientific papers in order to further explore some of the topics introduced during the course.

Educational objectives

GENERAL OBJECTIVES:
The aim of the course is to teach the main paradigms in many-body systems, particularly of fermionic systems, like electrons in metals, and to give an introduction to the methods of field theory in conndensed matter. At the end of the course the student should have acquired both technical competences (second quantization, Green function and Feynman diagrams at T=0 and T>0, response functions) and the physical understanding of the simplest approximations used to describe the many-body effects. In general the student should be able to understand both the language and the issues of modern research in correlated systems.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) Basic concepts of Landau Fermi liquid theory, the fundamental paradigm of the metallic state
OF 2) Properties of the Green functions and their physical meaning
OF 3) Interaction representation. S matrix. Wick's theorem and Feynman diagrams.
OF 4) Self-energy and Dyson equation. Hartree-Fock approximation, RPA approximation
OF 5) Linear response theory; response function. Analytic properties. Reactive and absorptive part.
OF 6) Kramers-Kronig relations. Kubo formula Fluctuation and dissipation theorem
B - Application skills
OF 7) The second objective is to prepare the students to actively solve problems in physics where MB theory concepts are required. This will happen at first with problems structured within a conceptual scheme similar to the ones discussed and applied during the course. However, as their preparation progresses, students are also expected to use MB concepts for solving new problems in different applications.
C - Autonomy of judgment
OF 8) The third and more ambitious objective is to teach the students to think using concepts and methods from MB theory as a powerful problem solving tool in physics.
D - Communication skills
OF 9) Besides having a clear understanding of the new acquired concepts in MB theory, the students should correspondingly acquire the ability to communicate and transmit these concepts in a clear and direct way.
E - Ability to learn
OF 10) The students should become able to read and understand scientific books and articles where MB concepts are involved and should be able to deepen autonomously their knowledge in this field.

Educational objectives

GENERAL OBJECTIVES:

This course will introduce the student to the most important concepts, ideas and tools of quantum field theory which has become the universal framework to describe all fundamental forces in nature. The student will understand how to construct field theories, quantize them in the presence of interactions and how to apply advanced techniques of regularization and renormalisation. Some special regard will be devoted to functional methods. The course will include the mathematical structure of non-Abelian gauge theories and their role in our present understanding of fundamental forces. The student will also have an elementary understanding of anomalies and their physical consequences in nature.

SPECIFIC OBJECTIVES:

A - Knowledge and understanding

The goal is for students to develop a critical understanding of the topics covered during the course, both as regards the purely theoretical aspects and in relation to the applications to different physical phenomena, and that they develop an adequate knowledge of the methods applied in theoretical physics, with particular reference to the methods usually used to conduct research in this sector.

B - Application skills

Alongside understanding the topics and methods used during the lessons, one of the objectives of the course is to enable students to apply those same methods to new problems, be they study or research.

C - Autonomy of judgment

One of the main objectives of the course is for students to develop critical skills with respect to the topics covered. They are often encouraged to follow other paths (than those followed during the lectures) for the achievement of results, or to propose interpretations or readings different from those presented by the teacher of the same results. Often during the lessons students are asked to make suggestions or make estimates in relation to specific calculations, with the aim of encouraging their autonomy of thought and their ability to make choices when confronted with delicate steps.

D - Communication skills

The course aims to increase students' communication skills, providing them with methodological tools that allow them to improve their ability to discuss in an original way topics related to theoretical and applicative aspects of quantum field theory.

E - Ability to learn

One of the most important objectives of the course is to provide students with a methodology that allows them to have access to a continuous updating of knowledge, trying in particular to increase their ability to deal with specialized literature.

Educational objectives

GENERAL OBJECTIVES:
This course will introduce students to the theory of classical and quantum information; elements of the algorithmic complexity theory; quantum computation and simulation; quantum cryptography. The student will study different experimental platforms to implement the protocols previously introduced.
At the end of the course, the student will be able, with a critical and analytical spirit, to formalize and analyze protocols of quantum communication and quantum computation. The ability to translate a quantum information processing task into an experimental platform will be developed, identifying its strengths and weaknesses.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1)To understand the fundamentals of information theory
OF 2) To understand the theory of quantum information
OF 3) To understand the language of quantum technologues

B - Application skills
OF 4) To be able to derive the evolution of a quantum circuit
OF 5) To be able to derive the evolution of an open quantum system
OF 6) To be able to model the different sources of noise present in a quantum information protocol
OF 7) To be able to define how to experimentally realize a quantum communication protocol
C - Autonomy of judgment
OF 8) To be able to exploit the knowledge acquired in quantum information for the implementation with different quantum technologies
D - Communication skills
OF 9) To know how to communicate in written reports an advanced concept
OF 10) To know how to present a recent research activity in the framework of quantum technologies
E - Ability to learn
OF 11) To be able to read independently scientific texts and articles in order to elaborate on the topics introduced in the course.

Educational objectives

To form the students on the following topics:
- linear response theory in solids
- light-matter interaction: quantum description of optical and infrared
spectroscopies
- impact of electron electron interaction on excitations: plasmon and
excitons
- charge transport in solids
- topological properties of solids

Educational objectives

Understanding the molecular basis of biological functions and the network of their interactions, both logical and physical, in the cell metabolism.

Educational objectives

GENERAL OBJECTIVES:
This course is designed as an introduction to computational biology and biophysics. It aims to bridge the gap between institutional learning and active research. The course is structured around three main aspects: i) TOPICS (principles, ideas); ii) METHODS (algorithms and computational techniques); iii) PERSPECTIVES of contemporary computational biology. Extensive reference and critical introductions to literature and current texts will be provided as guides for individual study. Efforts will be made to provide a clear framework of bibliographic references for each topic discussed, aiding in preparation for the final exam. At the end of the course, special guests will present original research lines of interest to students in biosystems, materials physics, and theoretical courses. By successfully completing the course, students will be able to navigate the world of computational biophysics at various scales (from molecules to cells) and master the main computation and analysis algorithms used in the field.

SPECIFIC OBJECTIVES:
A - Knowledge and Understanding
SO 1) Gain a historical-critical perspective of modern computational biology/biophysics
SO 2) Understand the fundamentals of modern evolutionary theory
SO 3) Gain practical experience with data analysis models based on Bayesian inference
SO 4) Gain direct experience with major bioinformatics databases (SwissProt, pFam, PDB,…)

B - Applied Skills
SO 7) Translate at least the main computational biophysics simulation and analysis algorithms into pseudo-code
SO 8) Improve programming skills in scripting languages (Python) or compiled languages (C/C++)
SO 9) Execute a molecular dynamics simulation of a small protein on GROMACS

C - Judgment Autonomy
SO 10) Evaluate the quality of a scientific article

D - Communication Skills
SO 11) Report the results of a research project to the class participants
SO 12) Actively participate in classroom discussions (in Italian and/or English)

E - Learning Skills
SO 13) Acquire fluency in consulting specific databases (e.g., PubMed, Google Scholar) to support/refute a research hypothesis
SO 14) Actively participate in the organization of self-learning groups

Educational objectives

GENERAL OBJECTIVES:
The course of Computational Statistical Mechanics aims to provide the necessary knowledge to understand and implement classical molecular dynamics and Monte Carlo techniques. The methods, that allow us to generate trajectories in phase space for sampling distinct statistical ensembles, will be studied. Some techniques which offer the possibility to calculate the free energy will be also discussed and it will be shown how the use of such results can provide a description of the atoms and molecules phase diagrams. At the end of the course, students will develop the ability of a quantitative reasoning and numerical skills useful for studying, modeling and understanding a large class of atomic and molecular systems as well as supramolecular aggregates. In addition, the student will be able to utilize the most common simulation packages which are available for a numerical study of complex systems, such as colloidal and bio-molecular systems, due to the acquired full knowledge of algorithms and numerical techniques on which these programs are built. Particular emphasis will be given to object-oriented and generic programming in the implementation of a computer simulation code. In particular, the modern C++ programming language will be introduced and discussed in the context of atomistic simulations. It will be also illustrated the use of the Python language, through the NumPy and MatPlotLib libraries, to analyze and visualize the data produced by computer simulations. During the course there will be also hands-on lectures, so that students will be able to put into practice the acquired knowledge through the implementation of their own simulation code. Students will be also stimulated to present the results obtained from the simulations, so as to test their ability to communicate clearly and effectively such results. The development of a numerical simulation code will be an opportunity for the students to design and develop their own project. This way they will be able to show their learning level and ability to apply independently the theoretical concepts acquired in the course.

SPECIFIC OBJECTIVES:

A - Knowledge and understanding
OF 1) Know common techniques to carry out computer simulations
OF 2) Know object oriented programming for scientific computations.
OF 3) Know common methods for analyzing data obtained from computer simulations.
OF 4) Understand data produced by computer simulations.

B - Application skills
OF 5) Ability to implement a simulation code.
OF 6) Ability to exploit simulations to obtain information about the physical properties of investigated systems.
OF 7) Be able to develop computer codes for analyzing data produced by computer simulations.

C - Autonomy of judgment
OF 8) Be able to critically analyze the results of “numerical experiments”.
OF 9) Be able to integrate autonomously the acquired knowledge in order to face new problems that require additional numeric techniques.
OF 10) Be able to identify the best technique to solve and study a physical problem numerically.

D - Communication skills
OF 11) Know how to communicate clearly to specialists and non-specialists, through manuscripts and presentations, the results obtained.
OF 12) Know how to clearly discuss a scientific topic.
OF 13) Know how to reproduce calculations related to a given scientific topic in a critical and informed manner.
E - Ability to learn
OF 14) Have the ability to learn new algorithms and numerical techniques by exploiting the scientific literature.
OF 15) Be able to conceive and develop their own project consisting of writing a simulation code or implementing a numerical technique.
OF 16) Be able to overcome difficulties and setbacks in the implementation of numerical techniques through original ideas and solutions.

Educational objectives

GENERAL OBJECTIVES:
The aim of the course 'Computational Solid State Physics' is to provide both theoretical and practical understanding with the two main numerical approaches currently in use for the solution of the quantum many body problem in condensed matter physics:

a) Density Functional Theory, which allows to obtain predictions from first principles of electronic states, structural energies, and interatomic forces in molecules and solids;
b) Quantum Monte Carlo methods - variational, diffusion, path-integral – which can be applied to the numerical study of various many-body quantum systems (liquid or solid helium, electron gas, electrons in atoms and molecules).

SPECIFIC OBJECTIVES:
A- Knowledge and Understanding:
OF1: To know and understand the fundamentals of Hartree-Fock (H-F) theory.
OF2: To know and understand the fundamentals of Density Functional Theory (DFT).
OF3: To know and understand the fundamentals of Pseudopotential theory (PPT).
OF4: To know and understand the DFT+PPT theory of crystalline systems.
OF5: To know and understand the variational Monte Carlo (MC) method for identical particles.
OF6: To know and understand the "projection MC" method for identical particles.
OF7: To know and understand the path integral Monte Carlo (PIMC) method.
OF8: To know and understand the "sign problem" for systems of many identical fermions.
B- Application Skills:
OF9: To apply DFT+PPT to simple solid-state systems (using software like Quantum Espresso).
OF10: To apply various quantum Monte Carlo methods to simple systems of many identical bosons or fermions (writing simple C codes and using large pre-existing FORTRAN codes).
C- Autonomy of Judgement:
OF11: To be able to assess, for a real quantum solid or fluid, which theories and algorithms presented in the course are suitable for describing and/or predicting which physical properties.
OF12: To be able to evaluate the feasibility, in terms of memory and CPU time, of a numerical project in molecular or solid-state physics.
D- Communication Skills:
OF13: To be able to present the results of a theoretical-numerical project.
OF14: To be able to write concise reports on the results of a theoretical-numerical project.
Ability to Learn:
OF15: To progress autonomously in C programming skills.
OF16: To progress autonomously in the use of existing software and codes.
OF17: To progress in graphical visualization skills of one's own results.
OF18: To progress in the ability to read reviews and research articles.

Educational objectives

GENERAL OBJECTIVES:
The main objective of Advanced Mathematical Methods for Physics is that of providing an introduction to up-to-date computational methods that are used in research areas of current interest. Three different courses are offered.

The goal of the third course is to provide the students with the theoretical background of perturbative and asymptotic analysis used in many fields of theoretical physics:
a) Definition and properties of the perturbative and asymptotic exapansions used in theoretical physics;
b) Introduction to some asymptiotic methods --- Boundary Layers, WKB, Multiple Scale, Renormalization Group --- and analisys of their filds of applicability.
SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) To know and understand the foundations of the perturbative methods
OF 2) To know and understand the foundations asymptotic analysis
OF 3) To know and understand the Boundary Layer Theory
OF 4) To know and understand the WKB method
OF 5) To know and understand the Multiple Scale method
OF 6) To know and understand the Renormalization Group and it connections with asymptotica analysis.

B - Application skills
OF 7) Application of the asymptotic analysis to the solution of comlex problems
OF 8) Application of the Boundary Layer Theory, WKB method and Multiple Scale method to the study of simple problems.
OF 9) Application of the Renormalization Group method to the asymptotic analysis of the solution of simple ordinary differential equations.

C - Autonomy of judgment
OF 10) Ability to analize a simple perturbative problem.
OF 11) Ability to evaluate the structure of a simple perturbative problem and use the more appropriate method to its study.
D - Communication skills
OF 12) Ability to create an effective presentation of the results of a theoretical project
OF 13) Ability to present the basis of the asymptotic analysis and some of its methods.
E - Ability to learn
OF 14) Autonomous improvement in the study of perturbation method
OF 15) Autonomous improvement in the use of asymptotic analysis in more comlex problems
OF 16) Autonomous improvement in reading and understanding research articles and reviews

Educational objectives

This course analyzes the theory of phase transitions and of critical
phenomena. We develop in detail the theory of the Renormalization
Group of statistical systems, both with regard to the so-called
renormalization group in real space and to the one in momentum
space. The course will lead to an awareness of the general ideas that
are the basis of the theory of phase transitions and to a mastery of
the detailed techniques that allow for the development of the
necessary calculations.

Educational objectives

The student will acquire knowledge of the fundamental principles of light-matter interaction studied via semi-classical and quantum approaches. Moreover, the student will study different aspects related to the quantum mechanical nature of light and its characterization according to photon statistics. During the course, the student will also deal with non-linear optics and will study some practical applications of quantum optics.
A - Knowledge and understanding
OF 1) To understand the fundamentals of quantum optics and non linear optics.
OF 3) To understand phenomena related to light-matter interaction, using both semi-classical and quantum approaches.
B - Application skills
OF 4) To be able to use semi-classical and quantum approaches to understand phenomena related to the interaction of light with matter.
OF 5) To be able to apply the basic principles of quantum optics to solve simple problems related to the knowledge acquired during the course.
C - Autonomy of judgment
OF 6) To be able to evaluate which optical phenomena require a classical or quantum treatment of the electromagnetic field to be explained.
OF 7) To develop quantitative reasoning abilities and problem-solving skills, which represent the basis to study, model and understand quantum phenomena related to light-matter interaction.
D - Communication skills
OF 8) To know how to communicate the knowledge acquired during the course via presentation of a scientific work related to one particular topic discussed during the lecture.
E - Ability to learn
OF 9) Have the ability to consult scientific papers in the field of quantum optics.
OF 10) Have the ability to understand practical applications that use the basic principles of quantum optics.

Educational objectives

GENERAL OBJECTIVES:
The Molecular Biology course is designed to provide students the conceptual and methodological basis required to study the molecular mechanisms regulating gene expression in physiological and pathological conditions, including epigenetics. In addition to the knowledge on the structure and metabolism of nucleic acids, the course will introduce the most relevant techniques of DNA cloning, DNA and RNA manipulation and the applications of Genetic Engineering to basic research and biomedicine. Topics discussed will also include the recent generation of sequencing technologies in light of their importance for the recent annotation of emerging noncoding RNA genes. The discovery of long noncoding and circular RNAs will be also discussed as well as the in vivo approaches used to study their functional role (practical examples taken from recent literature will be used). The course will include lectures and seminars. By the end of the course, students will be able to apply the acquired knowledge to the study of the basic mechanisms of gene expression, as well as of complex processes such as development, cell division and differentiation, and to exploit them for a practical use in both basic and applied research.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) to know the mechanisms of regulation of gene expression and the technological methods available to intervene on it;
OF 2) to know the structure and function of the genome in humans and in the main model systems;
OF 3) to know the origin and the maintenance of the biological complexity;
OF 4) to understand the influence of the modern sequencing technologies for a better description and for the study of transcriptome dynamics in humans and in the main model systems;
OF 5) to understand the network of interactions between the biological molecules in the mechanisms of regulation of gene expression.

B - Application skills
OF 6) To be able to discriminate techniques to apply according to the different problems to be dealt with in the molecular biology field

C - Autonomy of judgment
OF 7) To be able to use the specific terminology;
OF 8) To be able to interpret the biological phenomena in a multi-scale and multi-factorial context;
OF 9) To be able to interpret the results of genomic studies

D - Communication skills
OF 10) To know how to report papers already present in the literature in the form of an oral presentation

E - Ability to learn
OF 11) Have the ability to search and consult the scientific literature in the main biological databases
OF 12) Have the ability to evaluate the importance and the stringency of the published data

Educational objectives

General Objectives:
To acquire knowledge of fundamental topics in Mathematical Physics and the related mathematical methods.

Specific Objectives:

Knowledge and Understanding:

By the end of the course, students will be familiar with the fundamentals of operator theory in Hilbert spaces, the mathematical structure of quantum mechanics, and the basic methods for studying problems in quantum mechanics from the perspective of mathematical physics.

Applying knowledge and understanding:

Students who pass the exam will be able to: i) apply the results of operator theory, ii) construct self-adjoint Hamiltonians and study their spectra, iii) rigorously approach a scattering problem, iv) understand the mathematical methods required for the study of the dynamics of many-body systems, with particular regard to the phenomenon of condensation.

Critical Thinking and Judgment:

Students who pass the exam will be able to recognize a mathematical-physical approach and analyze similarities and differences compared to the typical approach in Theoretical Physics.

Communication Skills:

Students who pass the exam will have developed the ability to communicate concepts, ideas, and methodologies in mathematical physics.

Learning Skills:

The knowledge acquired will enable students to pursue further study—either independently or through other courses—on more specialized aspects of the methods of mathematical physics.

Educational objectives

Formative targets:

The objectives of the course are to bring the student to a deep knowledge and understanding of the basic mathematical properties i) of the nonlinear wave propagation with or without dispersion or dissipation; ii) of the construction of nonlinear mathematical models of physical interest, through the multiscale method, like the soliton equations, and of the mathematical techniques to solve them, arriving to the introduction of current research topics in the theory of solitons and anomalous waves. At the end of the course the student must be able i) to apply the acquired methods to problems in nonlinear physics even different from those studied in the course, in fluid dynamics, nonlinear optics, theory of gravitation, etc .., solving typical problems of the nonlinear dynamics; ii) to integrate in autonomy the acquired knowledges through the suggested literature, to solve also problems of interest for him/her, and not investigated in the course. The student will have the ability to consult supplementary material, interesting scientific papers, having acquired the right knowledges and critical skill to evaluate their content and their potential benefits to his/her scientific interests. At last the student must be able to conceive and develop a research project in autonomy. In order to achieve these goals, we plan to involve the student, during the theoretical lectures and exercises, through general and specific questions related to the subject; or through the presentation in depth of some specific subject agreed with the teacher.

Educational objectives

A - Knowledge and understanding
OF 1) Starting from the study of neurobiology of the nervous system, the student will first concentrate on the mechanisms regulating the electro-chemical properties of nerve cells and their connections, eventually studing the dynamics of populations of neuronal networks. The knowledge acquired will be on nonlinear and statistical physics compared to experimental data.
OF 2) The students will develop generally applicable skills in the field of theoretical physics of the complex systems and the nonlinear dynamics.
B - Application skills
OF 3) The student will be able to understand the dynamics of neuronal populations at the basis of the cognitive functions like decision making and short-term memory.
OF 4) The student will be able to apply analysis techniques and methods to electrophysiological data.
C - Autonomy of judgment
OF 5) By attending the lessons and with the regular interaction during the lessons themselves, the student will develop adequate autonomy of judgment, as he/she will be able to interface constantly with the teacher and critically analyze the information learned.
D - Communication skills
OF 6) The skills on the neurobiology of the nervous system will allow the student to interact with environments different from physics, enabling him/her to initiate multidisciplinary interactions in the life sciences.
E - Ability to learn
OF 7) The student will have the ability to evaluate and solve various problems of both data analysis and physics of complex systems.
OF 8) The acquired knowledge will allow the student to tackle the study of interdisciplinary papers on the physical phenomena underlying the behavior of the nervous system.

Educational objectives

GENERAL OBJECTIVES:
The goal of the course is the study of the foundations of the
statistical mechanics
of non equilibrium systems, with special enphasis on stochastic
models (e.q. Langevin equations)
i) to provide the student with a deep knowledge and understanding of
these
concepts, and
ii) to allow him (her) to successfully apply them in various physical
contexts. In particular, the student must be able to
use techniques of integration in the complex domain in all the
physical contexts in which they have applications.

SPECIFIC OBJECTIVES:

A - Knowledge and understanding
- To know the basis of the kinetic theory
- To understand how to use stochastic processes

B - Application skills
- To know the theory of fluctuations and the linear response

C - Autonomy of judgment
- To be able to integrate the knowledge acquired in order to apply it in
the more general context of statistical mechanics

E - Ability to learn
- To be able to read independently scientific texts and articles in
order to elaborate on the topics introduced in the course.

Educational objectives

GENERAL OBJECTIVES:
Provide fundamental notions of: ultrashort pulses generation and propagation in linear and non-linear media, characterization of time and frequency, spatial and polarization profiles. Pinpoint selected examples of ultrafast processes in physics, chemistry and biology (molecular switches, photoreceptors isomerization, photoinduced processes in
hemeproteins). Highlight novel approaches to non linear imaging and
related instrumentation. Hands on laboratory tutorials.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) To know photonics foundations and its most common application
OF 2) To understand non linear processes relevant for propagation of light pulses in materials
OF 3) Understand principles of non-linear spectroscopy illustrated by Feynman diagrams

B - Application skills
OF 4) Learn how to apply equations for linear and non linear propagation to real cases such as short pulses in optical fibers.
OF 5) Solve problems related to evaluation of cross sections for linear and non linear spectroscopies
OF 6) To be able to apply numerical techniques for the evaluation of radiation – matter interaction

C - Autonomy of judgment
OF 7) To be able to apply in the future the acquired skills to complex problems in photochemistry and photobiology

D - Communication skills
OF 8) To know how to communicate the critical steps necessary to solve elementary problems dealing with spectroscopy and light matter interaction in non linear regime

E - Ability to learn
OF 9) Have the ability to autonomously consult scientific articles to expand the knowledge developed in the course

Educational objectives

GENERAL OBJECTIVES:
The course in Physics of Liquids aims to provide the necessary knowledge
to understand the disordered state of matter. Emphasis will be directed toward the
connection between the inter-particle interaction potential and the resulting
equilibrium structure. The themes of short-range ordering
and of the dynamics in the fluid and glass phases
will be studied in depth. At the end of the course, students will develop quantitative reasoning skills and analytical abilities useful for studying, modelling and understanding phenomena related to disordered soft matter.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) To know the theory of classical fluids, from mean field models, to integral theories and perturbative approaches.
OF 2) To understand the physical basis of the integral closures.
OF 3) To know how to extract structural and dynamical quantities from the scattering of X rays and neutrons.
OF 4) Know how to go from a microscopic theory to a hydrodynamic theory.
B - Application skills
OF 5) To be able to compute the cluster integrals that compose the virial coefficient for simple interaction potentials.
OF 6) To be able to solve the equations governing the structure of a fluid in the presence of external fields.
OF 7) To be able to apply perturbative techniques
…
C - Autonomy of judgment
OF 8) To be able to understand the results of experiments and simualtions on simple and complex liquids.
OF 9) To be able to integrate the knowledge acquired in order to choose the best closure relations for a particular problem.
D - Communication skills
OF 10) To know how to communicate the results of experiments and simulations on simple liquids.

E - Ability to learn
OF 11) Have the ability to consult and understand books and articles in order to gain a deeper knowledge of the topics discussed during the course.

Educational objectives

GENERAL OBJECTIVES:
Nanophotonics and Spectroscopic Methods" course aims to provide the necessary knowledge on spectroscopic and nanophotonics techniques in condensed matter to understand the characteristics of materials from the point of view of electronic, reticular and vibrational degrees of freedom both at equilibrium and out of equilibrium. Different spectroscopic techniques: neutron scattering, scattering and absorption of electromagnetic radiation, will be studied within the formalism of the scattering matrix S and the linear response theorem. It will be understood how from these techniques it is possible to study the spectrum of fundamental excitations in condensed matter such as the phonon spectrum, the electronic absorption of free particles, the effects of the superconductive transition in electromagnetic properties, the vibrational transitions in liquids and biophysical systems. At the end of the course, students will develop quantitative reasoning skills and analytical resolution skills useful for studying, modeling and understanding phenomena related to the electronic and vibrational properties of condensed m

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) Know the fundamentals of the different spectroscopies in the linear response
OF 2) To understand how to obtain the spectrum of the relevant excitations of dense and diliut liquids and crystalline solides.
OF 3) Understanding the principles of the interaction between radiation and matter neutrons matter

B - Application skills
OF 4) Learn how to choose the most advantageous spectroscopic technique for the study of specific condensed matter problems
OF 5) Understanding the complementarity between spectroscopic techniques
OF 6) Be able to understand the potential and experimental limitations of the various techniques considered

C - Autonomy of judgment
OF 7) To be able to apply in the future the acquired skills to the more general context of condensed matter physics

D - Communication skills
OF 8) Knowing how to communicate the basic concepts of the different spectroscopic techniques and the results potentially obtainable in the various fields.

E - Ability to learn
OF 10) Have the ability to autonomously consult basic textbooks and in some cases scientific articles to expand the knowledge developed in the course

Educational objectives

GENERAL OBJECTIVES:
Acquire familiarity with advanced deep learning techniques based on differentiable neural network models with supervised, unsupervised and reinforced learning paradigms; acquire skills in modelling complex problems through deep learning techniques, and be able to apply them to different application contexts in the fields of physics and basic and applied scientific research.

Discussed topics include: general machine learning concepts, differentiable neural networks, regularization techniques. Convolutional neural network, neural network for sequence analysis (RNN, LSTM / GRU, Transformers). Advanced learning techniques: transfer learning, domain adaptation, adversarial learning, self-supervised and contrastive learning, model distillation.
Graph Neural Networks (static and dynamic) and application to structured models for physics: dynamic models, simulation of complex fluids, GNN Hamiltonians and Lagrangians. Generative and variational models: variational mean-field theory, expectation maximization, energy based and maximum entropy models (Hopfield networks, Boltzman machines and RBM), AutoEncoders, Variational AutoEncoders, GANs, Autoregressive flow models, invertible networks, generative models based on GNN. Quantum Neural Networks.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) Knowledge of the functioning of neural networks and their mathematical interpretation as universal approximators
OF 2) Understanding of the limits and potential of advanced machine learning models
OF 3) Understanding of the limits and potential of DL in solving physics problems

B - Application skills
OF 4) Design, implementation, commissioning and analysis of deep learning architectures to solve complex problems in physics and scientific research.

C - Autonomy of judgment
OF 5) To be able to evaluate the performance of different architectures, and to evaluate the generalization capacity of the same

D - Communication skills
OF 6) Being able to clearly communicate the formulation of an advanced learning problem and its implementation, its applicability in realistic contexts
OF 7) Being able to motivate and to evaluate the generalization capacity of a DL model

E - Ability to learn
OF 8) Being able to learn alternative and more complex techniques
OF 9) Being able to implement existing techniques in an efficient, robust and reliable manner

Educational objectives

A - Knowledge and understanding
OF 1) To possess a basic knowledge of complexity science, i.e. the collective properties that emerge with a large number of interacting components (atoms, particles or bacteria in a physical or biological context, or people, machines or businesses in a socio-economic context).
OF 2) Understanding the mechanisms underlying the emergence of complex macroscopic properties from knowledge of microscopic mechanisms.
OF 3) Mastering the basic toolbox of a complexity scientist: information theory, network theory, scale invariance and critical phenomena, properties of dynamical systems, agent models.
B - Application skills
OF 4) Knowing how to devise simple models for complex phenomenologies.
OF 5) Being able to tackle complex problems analytically or computationally, translating research questions into concrete solution and verification actions.
OF 6) Being able to apply the techniques and methods learnt also outside the areas covered in the course.
OF 7) Integrating the knowledge acquired in order to formalise problems and obtain results and predictions of increasing accuracy.
C - Autonomy of judgment
OF 8) Being able to analyse phenomena, also through the acquisition of data and evidence, that fall within the scope of complexity and identify their essential elements.
OF 9) Being able to synthesise phenomenologies in order to be able to distill relevant and relevant questions.
OF 10) Being able to identify interesting new research directions.
D - Communication skills
OF 11) Being able to communicate complex issues in a simple way, focusing on the essential elements and revealing cause-effect relationships as far as possible.
OF 12) Being able to organise a coherent, profound yet comprehensible presentation.
OF 13) Knowing how to express one's thoughts in a way that stimulates group work and interaction with colleagues.
E - Ability to learn
OF 14) Have the ability to consult reference texts and articles.
OF 15) Being able to assess the relevance of results, their place in the scientific panorama of reference and their potential importance for the research topics of interest.
OF 16) Being able to design and develop a research project, identifying the main objectives and the possible paths to reach them.

Educational objectives

This course analyzes the theory of phase transitions and of critical
phenomena. We develop in detail the theory of the Renormalization
Group of statistical systems, both with regard to the so-called
renormalization group in real space and to the one in momentum
space. The course will lead to an awareness of the general ideas that
are the basis of the theory of phase transitions and to a mastery of
the detailed techniques that allow for the development of the
necessary calculations.

Educational objectives

GENERAL OBJECTIVES:
The course is an advanced module aimed at guiding the students through a journey at the boundary between statistical physics and machine learning by introducing advanced concepts of equilibrium and out of equilibrium statistical mechanics and by illustrating their applications to learning models and development of artificial intelligence.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) To acquire the main methods of statistical mechanics, probability and information theory relevant to applications in machine learning and inference, such as the replica approach, message passing, mutual information, data compression, Bayesian approaches
OF 2) To understand the different physical behaviour shown by inference and artificial learning procedures (curse of dimensionality, metastability, presence of multiple thermodynamic states)
B - Application skills
OF 3) To know how to apply an analytical technique to a given inference or learning setting to study its physical behavior
C - Autonomy of judgment
OF 4) Be able to recognize to which class of disordered systems a given inference or learning setting belongs
D - Communication skills
OF 5) Ability to learn from oral presentation of research results on topics similar to those introduced during the course
OF 6) Ability to present the course topics orally in a non-technical language that allows understanding even by those who have not yet taken the course
E - Ability to learn
OF 7) To be able to read scientific texts and articles in order to independently investigate the topics introduced during the course

Educational objectives

GENERAL OBJECTIVES:
The aim of the course is to teach the main paradigms in many-body systems, particularly of fermionic systems, like electrons in metals, and to give an introduction to the methods of field theory in conndensed matter. At the end of the course the student should have acquired both technical competences (second quantization, Green function and Feynman diagrams at T=0 and T>0, response functions) and the physical understanding of the simplest approximations used to describe the many-body effects. In general the student should be able to understand both the language and the issues of modern research in correlated systems.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) Basic concepts of Landau Fermi liquid theory, the fundamental paradigm of the metallic state
OF 2) Properties of the Green functions and their physical meaning
OF 3) Interaction representation. S matrix. Wick's theorem and Feynman diagrams.
OF 4) Self-energy and Dyson equation. Hartree-Fock approximation, RPA approximation
OF 5) Linear response theory; response function. Analytic properties. Reactive and absorptive part.
OF 6) Kramers-Kronig relations. Kubo formula Fluctuation and dissipation theorem
B - Application skills
OF 7) The second objective is to prepare the students to actively solve problems in physics where MB theory concepts are required. This will happen at first with problems structured within a conceptual scheme similar to the ones discussed and applied during the course. However, as their preparation progresses, students are also expected to use MB concepts for solving new problems in different applications.
C - Autonomy of judgment
OF 8) The third and more ambitious objective is to teach the students to think using concepts and methods from MB theory as a powerful problem solving tool in physics.
D - Communication skills
OF 9) Besides having a clear understanding of the new acquired concepts in MB theory, the students should correspondingly acquire the ability to communicate and transmit these concepts in a clear and direct way.
E - Ability to learn
OF 10) The students should become able to read and understand scientific books and articles where MB concepts are involved and should be able to deepen autonomously their knowledge in this field.

Educational objectives

GENERAL OBJECTIVES:
The course aims to provide the necessary knowledge of the operating principles of the instrumentation used in biomedical research and diagnostics. In particular, the students study the interactions of ionizing and non-ionizing radiation with matter and learn how to exploit them in imaging techniques. The knowledge of radiography and tomography with X and gamma rays, with magnetic resonance and ultrasound is acquired.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) To know the fundamentals of radiation-material interactions in biomedicine.
OF 2) To learn about physical methods for imaging and the biological effects of radiation in medicine.
OF 3) To understand image reconstruction algorithms in diagnostics and research.
OF 4) To know the equipments used for imaging in biomedicine.
OF 5) To understand radiation detectors in medicine.
…
B - Application skills
OF 6) To Know how to deduce the response of the detectors used in biomedicine.
OF 7) To be able to solve problems related to the interaction of ionizing radiation and matter.
…
C - Autonomy of judgment
OF 8) To be able to integrate the knowledge acquired in order to apply them for diagnostics and research in the health sector.

D - Communication skills

E - Ability to learn
OF 9) Have the ability to consult scientific articles in order to independently investigate topics in the health sector.
OF 10) Be able to conceive and develop a related diagnostic imaging project in biomedicine.

Educational objectives

A - Knowledge and understanding
OF 1) To possess a basic knowledge of complexity science, i.e. the collective properties that emerge with a large number of interacting components (atoms, particles or bacteria in a physical or biological context, or people, machines or businesses in a socio-economic context).
OF 2) Understanding the mechanisms underlying the emergence of complex macroscopic properties from knowledge of microscopic mechanisms.
OF 3) Mastering the basic toolbox of a complexity scientist: information theory, network theory, scale invariance and critical phenomena, properties of dynamical systems, agent models.
B - Application skills
OF 4) Knowing how to devise simple models for complex phenomenologies.
OF 5) Being able to tackle complex problems analytically or computationally, translating research questions into concrete solution and verification actions.
OF 6) Being able to apply the techniques and methods learnt also outside the areas covered in the course.
OF 7) Integrating the knowledge acquired in order to formalise problems and obtain results and predictions of increasing accuracy.
C - Autonomy of judgment
OF 8) Being able to analyse phenomena, also through the acquisition of data and evidence, that fall within the scope of complexity and identify their essential elements.
OF 9) Being able to synthesise phenomenologies in order to be able to distill relevant and relevant questions.
OF 10) Being able to identify interesting new research directions.
D - Communication skills
OF 11) Being able to communicate complex issues in a simple way, focusing on the essential elements and revealing cause-effect relationships as far as possible.
OF 12) Being able to organise a coherent, profound yet comprehensible presentation.
OF 13) Knowing how to express one's thoughts in a way that stimulates group work and interaction with colleagues.
E - Ability to learn
OF 14) Have the ability to consult reference texts and articles.
OF 15) Being able to assess the relevance of results, their place in the scientific panorama of reference and their potential importance for the research topics of interest.
OF 16) Being able to design and develop a research project, identifying the main objectives and the possible paths to reach them.

Educational objectives

GENERAL OBJECTIVES:
The main objective of the course is to illustrate the characteristics of some of the best known disordered models and to introduce the approximations and analytical techniques that allow their study in statistical mechanics.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) To know the main disordered models, such as dilute ferromagnets, ferromagnets with random external field, and spin glasses
OF 2) To understand the different physical behaviors that arise as a result of the introduction of quenched disorder (slowing down of the dynamics, metastability, presence of many thermodynamic states).
OF 3) To know the main techniques of statistical mechanics (mean-field approximations, replica and cavity methods) that allow the analytical study of models with disorder.

B - Application skills
OF 4) To know how to apply an analytical technique (mean-field approximation, replica and cavity method) to a given Hamiltonian to study its physical behavior.
C - Autonomy of judgment
OF 5) Be able to recognize to which class of disordered systems a given Hamiltonian belongs.

D - Communication skills
OF 6) Ability to present the course topics orally in a non-technical language that allows understanding even by those who have not yet taken the course.
E - Ability to learn
OF 7) To be able to read scientific texts and articles in order to independently investigate the topics introduced during the course.

Educational objectives

GENERAL OBJECTIVES:

The Surface Physics and Nanostructures course aims to provide the knowledge of the structural properties of solid systems at low dimensional scale and to understand their characteristics from the point of view of both electronic and vibrational degrees of freedom. The optical properties of nanostructured semiconductor systems and magnetic properties of nanostructured metal systems will then be analyzed.
At the end of the course, students will be able to transpose the knowledge of 3D solid state physics to two-dimensional and one-dimensional systems and have an in-depth knowledge of the frontier topics in nanosciences. These acquisitions will be verified also thanks to the presentation of the topics in seminars held by the students.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) To know the properties of low-dimensional solid systems
OF 2) To understand the effects of reduced dimensionality
OF 3) To know the most advanced techniques for studying the low-dimensional systems
B - Application skills
OF 4) To be able to deduce the properties of a surface or a nanostructure
OF 5) To be able to choose the correct technqiue to investigate a surface or a nanostructure
C - Autonomy of judgment
OF 6) To be able to autonomously individuate an experiment on low-dimensional systems
OF 7) To be able to integrate the acquired knowledge so to be able to face a scientific problem associated to low-dimensional systems
D - Communication skills
OF 8) To know how to communicate the properties of a low-dimensional system
OF 9) To be able to communicate the advantages of an advanced investigation

E - Ability to learn
OF 10) To have the ability to consult the specific scientific literature
OF 11) To be able to evaluate the specific scientific literature
OF 12) To be able to design and plan an experiment on low dimensional systems

Educational objectives

A - Knowledge and understanding
OF 1) To know the fundamentals of the theory of stochastic processes, discrete and continuous, and thier formal framework in terms of resolution of Chapman-Kolmogorov, Fokker-Planck and master equations.
OF 2) To understand the similarities with the properties of equations already known to the students (like Schroedinger equation) and to learn equation resolution methods using operational calculus.
OF 3) To know the formalism of stochastic integration of stochastic differential equations and the connection to the Fokker-Planck partial differential equation.
B - Application skills
OF 4) To deduce physical properties of systems from the analysis of the stochastic equations.
OF 5) To apply newly learned methods to the estimate of first passage times and to the consequences of Arrhenius law on relaxation towards equilibrium in systems with rough potential landscapes.
OF 6) To apply methods and techniques to systems of different nature at and off equilibrium (viscous liquids, wave systmes, glassy systems, lasers).
C - Autonomy of judgment
OF 7) To be able to integrate acquired knwoledge and apply it also to cases not explicitly treated in the course.
OF 8) To be able to connect acquired knowledge to previous one, formalizing known concepts and connetcing them to more complex cases.
D - Communication skills
OF 9) To know how to orally present a demonstration procedure or an application assessing the most relevant and clarifying steps and their meaning.
E - Ability to learn
OF 10) To be able to consult diferrent textbooks and scientifc papers to the aim of autonomously deepening some of the arguments covered by the course.
OF 11) To be able to evaluate the effectiveness of the various studied approaches in relation to the treated problems.

Educational objectives

GENERAL OBJECTIVES:
The goal of the course is the study of the foundations of Quantum Field Theory, starting from thee quantization of the free fields up to the introduction of the interaction of the Dirac field with the electromagnetic field (QED) and to the definition and calculation of a cross section at tree-level in perturbation theory.
The student will acquire the basic concepts of the quantization of the fields and he will be able to apply the Feynman rules for the calculation of a cross section at tree-level.
The know-how that the student acquires attending this course is indispensable for the advanced courses in Quantum Field Theory, in particular for the curriculum in Particle and Astroparticle Physics.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) Knowing the basis of the theory of classical and quantum fields, Lagrangian and Hamiltonian description. To be able to discuss the symmetries of a physical system and, accordingly, the conserved quantities.
OF 2) Understanding the basis of the canonical quantization and its applications to the free and interacting fields. To understand the scattering matrix.
OF 3) Knowing the definition and the basis of the calculation of a cross section.
B - Application skills
OF 5) Knowing the Feynman rules for the interaction of the Dirac and Electromagnetic fields (QED) and to be able to theoretically predict a cross section for a QED process at the tree-level in peruturbation theory.
C - Autonomy of judgment
OF 8) To be able to integrate the knowledge acquired in order to apply it in the more general context of Quantum Field Theory, renormalization and general higher-orders calculations in perturbation theory.
D - Communication skills
OF 10) Ability to discuss about the quantum theory of fields with the appropriate rigor and understanding of the approximations used

E - Ability to learn
OF 11) To be able to read independently scientific texts and articles in order to elaborate on the topics introduced in the course.

Educational objectives

GENERAL OBJECTIVES:
Aim of the course is to introduce the basic notions of the modern theory of gravity, and of its more important conceptual and astrophysical implications.

At the end of the course the student should: 1) have acquired the instruments of differential geometry which allow to formulate Einstein's equations and derive its predictions. 2) Have understood what is the role of the equivalence principle between gravitational and inertial mass in the formulation of the theory, and why the gravitational field modifies the spacetime geometry. 3) Have understood how to use the symmetries of a physical problem to simplify Einstein's equations and find solutions. 4) Be able to derive the solution describing the gravitational field external to a
non rotating, spherically symmetric body (the Schwarzschild solution), and to show that this solution can also represent a non rotating black hole. 5) Have understood how some of the main predictions of General Relativity can be obtained by solving the geodesic equations, which describe the motion of free particles in a gravitational field. 6) Have understood how to solve Einstein's equations in the weak field limit, to show that spacetime perturbations propagate as gravitational
waves.

Therefore, at the end of the course the student should: 1) be able to compute how vectors, one-forms and tensors transform under a coordinate transformation; to compute the covariant derivative of these geometrical objects and to solve exercises which involve these operations in tensor equations. 2) Be able to compute how does a vector change when parallely transported along a path in curved spacetime, and to derive the curvature tensor using this operation. 3) Be able to derive Einstein's equations. 4) Be able to derive and interpret some of the most interesting predictions of General Relativity: the gravitational redshift, light deflection near massive bodies, precession of Mercury perihelion, existence of gravitational waves.

This course introduces the fundamental concept of a curved spacetime due to the existence of a gravitational field, and discusses the more important aspects of the scientific revolution introduced by Einstein's theory. As such, it is a basic course for the laurea magistrale in Astronomy and Astrophysics, and it is also a matter which should be part of the cultural background of a modern physicist.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) Know the basics of differential geometry
OF 2) Know the basics of General Relativity and its most relevant concepts, including that of a black hole and gravitational waves
OF 3) Know and interpret the observational applications of the theo
B - Application skills
OF 4) Be able to perform analytical calculations of differential geometry
OF 5) Knowing how to derive Einstein's equations for the gravitational field
OF 6) Knowing how to derive and interpret some of the most important effects predicted by General Relativity
OF 7) Knowing how to calculate the geodetic motion in the spacetime of a black hole
C - Autonomy of judgment
OF 8) To fully understand the concept of curved spacetime, change of coordinates, and the consequences of the principles of Equivalence and General Covariance
D - Communication skills
OF 9) Knowing how to present in written and oral form the main derivations concerning formulas and theorems of differential geometry
OF 10) Knowing how to present in written and oral form the main derivations concerning General Relativity: Einstein equations, geodesic motion, metrics of a black hole, gravitational waves
E - Ability to learn
OF 11) Have the ability to apply the knowledge of the course to understand and derive more advanced topics

Educational objectives

GENERAL OBJECTIVES
The course “Advanced Optical Techniques and Applications” aims to provide the necessary knowledge on optical and photonic techniques that are most used in the field of applied physics. In particular, the sources of electromagnetic radiation, photonic components and devices and spectrometers most used in optical and photonic investigation techniques in the biomedical field, in cultural heritage, in image analysis, in industrial processes, in photovoltaics and in the chemical-physical analysis, will be discussed. Practical investigation experiences in these fields will be proposed in some laboratories of the department. At the end of the course, students will develop reasoning skills and quantitative resolution abilities useful for understanding and applying the optical and photonic techniques most used in the various fields of applied physics.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) Know the fundamentals of different photonic and optical techniques and their use in the various fields of applied physics;
OF 2) Understand the principles of interaction between radiation and matter and the use of specific electromagnetic sources;
OF 3) Understand the functioning of various photonic devices, various spectrometers and various spectroscopy and microscopy techniques;

B - Application skills
OF 4) Learn to choose the most advantageous photonic and/or optical technique for specific applications;
OF 5) Understand the complementarity between the various optical and photonic techniques;
OF 6) Be able to understand the potential and experimental limitations of the various techniques considered;

C - Autonomy of judgment
OF 7) Be able to integrate the knowledge acquired in order to apply it subsequently in the more general context of applied physics;

D – Communication skills
OF 8) Know how to communicate the basic concepts of the different photonic and optical techniques and the results potentially obtainable in the various fields;

E - Learning ability
OF 9) Have the ability to independently consult basic texts and scientific articles in order to independently study some topics introduced during the course.

Educational objectives

GENERAL OBJECTIVES:
The course aims to provide the necessary knowledge of the operating principles of the instrumentation used in biomedical research and diagnostics. In particular, the students study the interactions of ionizing and non-ionizing radiation with matter and learn how to exploit them in imaging techniques. The knowledge of radiography and tomography with X and gamma rays, with magnetic resonance and ultrasound is acquired.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) To know the fundamentals of radiation-material interactions in biomedicine.
OF 2) To learn about physical methods for imaging and the biological effects of radiation in medicine.
OF 3) To understand image reconstruction algorithms in diagnostics and research.
OF 4) To know the equipments used for imaging in biomedicine.
OF 5) To understand radiation detectors in medicine.
…
B - Application skills
OF 6) To Know how to deduce the response of the detectors used in biomedicine.
OF 7) To be able to solve problems related to the interaction of ionizing radiation and matter.
…
C - Autonomy of judgment
OF 8) To be able to integrate the knowledge acquired in order to apply them for diagnostics and research in the health sector.

D - Communication skills

E - Ability to learn
OF 9) Have the ability to consult scientific articles in order to independently investigate topics in the health sector.
OF 10) Be able to conceive and develop a related diagnostic imaging project in biomedicine.

Educational objectives

GENERAL OBJECTIVES: Understanding the fundamental optical and transport properties of semiconductors and using these properties in the main electronic and opto-electronic devices.

SPECIFIC OBJECTIVES:
A – Knowledge and understanding
OF 1) To know the fundamental electronic properties of semiconductors and how they derive from their crystalline structure and chemical composition.
OF 2) To understand how the fundamental electronic properties of semiconductors can be modified by material nanostructuring.
OF 3) To know the main charge transport phenomena in semiconductors.
OF 4) To know the main processes of interaction of light with semiconductors and related phenomena.
OF 5) Based on the previous points, learning the operating principles of the most common electronic and optoelectronic devices based on semiconductor materials.

B - APPLICATION SKILLS
OF 6) To know in general how to determine which semiconductor materials can be used to fabricate devices with specific characteristics.
OF 7) To know how to predict the effects of electromagnetic fields on the transport and optical properties of semiconductors.
OF 8) To be able to select a semiconductor device for the measurement of given quantities.
C – Autonomy of judgement
OF 9) To determine the connections between the properties of a semiconductor and the characteristics of a device.
OF 10) To be able to integrate the knowledge acquired in order to exploit it in the more general context of device applications of semiconductor materials.
D – Communication skills
OF 11) To know how to explain the fundamental reasons behind the functioning principle of a device.
OF 12) To know how to justify the choice of a semiconductor material for carrying out specific applications.
E – Ability to learn
OF 13) To acquire the ability to independently read and understand scientific texts and technical articles based on the topics covered in the course.
OF 14) To have the ability to choose and identify an appropriate device depending on the use.

Educational objectives

GENERAL OBJECTIVES:
This course will introduce students to the theory of classical and quantum information; elements of the algorithmic complexity theory; quantum computation and simulation; quantum cryptography. The student will study different experimental platforms to implement the protocols previously introduced.
At the end of the course, the student will be able, with a critical and analytical spirit, to formalize and analyze protocols of quantum communication and quantum computation. The ability to translate a quantum information processing task into an experimental platform will be developed, identifying its strengths and weaknesses.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1)To understand the fundamentals of information theory
OF 2) To understand the theory of quantum information
OF 3) To understand the language of quantum technologues

B - Application skills
OF 4) To be able to derive the evolution of a quantum circuit
OF 5) To be able to derive the evolution of an open quantum system
OF 6) To be able to model the different sources of noise present in a quantum information protocol
OF 7) To be able to define how to experimentally realize a quantum communication protocol
C - Autonomy of judgment
OF 8) To be able to exploit the knowledge acquired in quantum information for the implementation with different quantum technologies
D - Communication skills
OF 9) To know how to communicate in written reports an advanced concept
OF 10) To know how to present a recent research activity in the framework of quantum technologies
E - Ability to learn
OF 11) To be able to read independently scientific texts and articles in order to elaborate on the topics introduced in the course.

Educational objectives

GENERAL OBJECTIVES
The course “Advanced Computational Methods for Medical Physics” aims to provide the necessary knowledge on the computational techniques that are most used in the field of physics applied to medicine. In particular, the techniques currently used for "computational neuroimaging" will be discussed, that is, for the analysis of images obtained in the context of medical diagnostics, and the advanced simulation techniques with the Monte Carlo method for radiotherapy and neuroimaging. Practical investigation experiences in these fields will be proposed. At the end of the course, students will develop reasoning skills and quantitative resolution abilities useful for understanding and applying the aforementioned techniques.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) Know the fundamentals of the different computational neuroimaging techniques and of the Monte Carlo method applied to medical diagnostics;
OF 2) Understand the operating principles of the computational techniques involved;

B – Application skills
OF 3) Learn to choose the most advantageous computational technique for a given medical physics purpose;
OF 4) Understand the complementarity between the various computational techniques;

C - Autonomy of judgment
OF 5) Be able to integrate the knowledge acquired in order to apply it subsequently in the more general context of medical physics;

D – Communication skills
OF 6) Know how to communicate the basic concepts of the different computational techniques and the results potentially obtainable in the various fields;

E - Learning skills
OF 7) Have the ability to independently consult basic texts and scientific articles in order to independently study some topics introduced during the course.

Educational objectives

GENERAL OBJECTIVES:
The course aims to introduce the foundations of Superconductivity and Superfluidity. A preliminary part will be devoted to the phenomenological London and Ginzburg-Landau theories. The latter will be used to introduce the more general topic of spontaneous symmetry breaking in second-order phase transition, and the Anderson-Higgs mechanism for superconductivity. After discussion of the second-quantization for many-body fermionic and bosonic systems the focus will be on the microscopic models for superconductors (BCS Bardeen_Cooper e Schrieffer theory) and superfluids.
The final part will consist in a brief overview of current research topics on unconventional superconductors.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) To know the basis of the superconducting phenomenon, its phenomenological and microscopic description and its experimental applications
OF 2) To understand key concepts as spontaneous symmetry breaking and order parametr for a phase transition, with particular emphasis on continous symmetries.
OF 3) To know basic applications of second quantization to fermionic and bosonic many-particle systems
B - Application skills
OF 4) To be able to describe the superfluid phenomen both for fermions and bosons, and its theoretical and experimental implications
C - Autonomy of judgment
OF 5) To be able to integrate the knowledge acquired in order to apply in the more general context of unconventional superconduvtivity and interacting fermionic systems
E - Ability to learn
OF 6) Have the ability to read scientific papers in order to further explore some of the topics introduced during the course.

Educational objectives

GENERAL OBJECTIVES:
The course aims to provide the necessary knowledge of the operating principles of the instrumentation used in biomedical research and diagnostics. In particular, the students study the interactions of ionizing and non-ionizing radiation with matter and learn how to exploit them in imaging techniques. The knowledge of radiography and tomography with X and gamma rays, with magnetic resonance and ultrasound is acquired.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) To know the fundamentals of radiation-material interactions in biomedicine.
OF 2) To learn about physical methods for imaging and the biological effects of radiation in medicine.
OF 3) To understand image reconstruction algorithms in diagnostics and research.
OF 4) To know the equipments used for imaging in biomedicine.
OF 5) To understand radiation detectors in medicine.
…
B - Application skills
OF 6) To Know how to deduce the response of the detectors used in biomedicine.
OF 7) To be able to solve problems related to the interaction of ionizing radiation and matter.
…
C - Autonomy of judgment
OF 8) To be able to integrate the knowledge acquired in order to apply them for diagnostics and research in the health sector.

D - Communication skills

E - Ability to learn
OF 9) Have the ability to consult scientific articles in order to independently investigate topics in the health sector.
OF 10) Be able to conceive and develop a related diagnostic imaging project in biomedicine.

Educational objectives

GENERAL OBJECTIVES: Understanding the fundamental optical and transport properties of semiconductors and using these properties in the main electronic and opto-electronic devices.

SPECIFIC OBJECTIVES:
A – Knowledge and understanding
OF 1) To know the fundamental electronic properties of semiconductors and how they derive from their crystalline structure and chemical composition.
OF 2) To understand how the fundamental electronic properties of semiconductors can be modified by material nanostructuring.
OF 3) To know the main charge transport phenomena in semiconductors.
OF 4) To know the main processes of interaction of light with semiconductors and related phenomena.
OF 5) Based on the previous points, learning the operating principles of the most common electronic and optoelectronic devices based on semiconductor materials.

B - APPLICATION SKILLS
OF 6) To know in general how to determine which semiconductor materials can be used to fabricate devices with specific characteristics.
OF 7) To know how to predict the effects of electromagnetic fields on the transport and optical properties of semiconductors.
OF 8) To be able to select a semiconductor device for the measurement of given quantities.
C – Autonomy of judgement
OF 9) To determine the connections between the properties of a semiconductor and the characteristics of a device.
OF 10) To be able to integrate the knowledge acquired in order to exploit it in the more general context of device applications of semiconductor materials.
D – Communication skills
OF 11) To know how to explain the fundamental reasons behind the functioning principle of a device.
OF 12) To know how to justify the choice of a semiconductor material for carrying out specific applications.
E – Ability to learn
OF 13) To acquire the ability to independently read and understand scientific texts and technical articles based on the topics covered in the course.
OF 14) To have the ability to choose and identify an appropriate device depending on the use.

Educational objectives

A - Knowledge and understanding
OF 1) To possess a basic knowledge of complexity science, i.e. the collective properties that emerge with a large number of interacting components (atoms, particles or bacteria in a physical or biological context, or people, machines or businesses in a socio-economic context).
OF 2) Understanding the mechanisms underlying the emergence of complex macroscopic properties from knowledge of microscopic mechanisms.
OF 3) Mastering the basic toolbox of a complexity scientist: information theory, network theory, scale invariance and critical phenomena, properties of dynamical systems, agent models.
B - Application skills
OF 4) Knowing how to devise simple models for complex phenomenologies.
OF 5) Being able to tackle complex problems analytically or computationally, translating research questions into concrete solution and verification actions.
OF 6) Being able to apply the techniques and methods learnt also outside the areas covered in the course.
OF 7) Integrating the knowledge acquired in order to formalise problems and obtain results and predictions of increasing accuracy.
C - Autonomy of judgment
OF 8) Being able to analyse phenomena, also through the acquisition of data and evidence, that fall within the scope of complexity and identify their essential elements.
OF 9) Being able to synthesise phenomenologies in order to be able to distill relevant and relevant questions.
OF 10) Being able to identify interesting new research directions.
D - Communication skills
OF 11) Being able to communicate complex issues in a simple way, focusing on the essential elements and revealing cause-effect relationships as far as possible.
OF 12) Being able to organise a coherent, profound yet comprehensible presentation.
OF 13) Knowing how to express one's thoughts in a way that stimulates group work and interaction with colleagues.
E - Ability to learn
OF 14) Have the ability to consult reference texts and articles.
OF 15) Being able to assess the relevance of results, their place in the scientific panorama of reference and their potential importance for the research topics of interest.
OF 16) Being able to design and develop a research project, identifying the main objectives and the possible paths to reach them.

Educational objectives

GENERAL OBJECTIVES:

The Surface Physics and Nanostructures course aims to provide the knowledge of the structural properties of solid systems at low dimensional scale and to understand their characteristics from the point of view of both electronic and vibrational degrees of freedom. The optical properties of nanostructured semiconductor systems and magnetic properties of nanostructured metal systems will then be analyzed.
At the end of the course, students will be able to transpose the knowledge of 3D solid state physics to two-dimensional and one-dimensional systems and have an in-depth knowledge of the frontier topics in nanosciences. These acquisitions will be verified also thanks to the presentation of the topics in seminars held by the students.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) To know the properties of low-dimensional solid systems
OF 2) To understand the effects of reduced dimensionality
OF 3) To know the most advanced techniques for studying the low-dimensional systems
B - Application skills
OF 4) To be able to deduce the properties of a surface or a nanostructure
OF 5) To be able to choose the correct technqiue to investigate a surface or a nanostructure
C - Autonomy of judgment
OF 6) To be able to autonomously individuate an experiment on low-dimensional systems
OF 7) To be able to integrate the acquired knowledge so to be able to face a scientific problem associated to low-dimensional systems
D - Communication skills
OF 8) To know how to communicate the properties of a low-dimensional system
OF 9) To be able to communicate the advantages of an advanced investigation

E - Ability to learn
OF 10) To have the ability to consult the specific scientific literature
OF 11) To be able to evaluate the specific scientific literature
OF 12) To be able to design and plan an experiment on low dimensional systems

Educational objectives

GENERAL OBJECTIVES:
This course will introduce students to the theory of classical and quantum information; elements of the algorithmic complexity theory; quantum computation and simulation; quantum cryptography. The student will study different experimental platforms to implement the protocols previously introduced.
At the end of the course, the student will be able, with a critical and analytical spirit, to formalize and analyze protocols of quantum communication and quantum computation. The ability to translate a quantum information processing task into an experimental platform will be developed, identifying its strengths and weaknesses.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1)To understand the fundamentals of information theory
OF 2) To understand the theory of quantum information
OF 3) To understand the language of quantum technologues

B - Application skills
OF 4) To be able to derive the evolution of a quantum circuit
OF 5) To be able to derive the evolution of an open quantum system
OF 6) To be able to model the different sources of noise present in a quantum information protocol
OF 7) To be able to define how to experimentally realize a quantum communication protocol
C - Autonomy of judgment
OF 8) To be able to exploit the knowledge acquired in quantum information for the implementation with different quantum technologies
D - Communication skills
OF 9) To know how to communicate in written reports an advanced concept
OF 10) To know how to present a recent research activity in the framework of quantum technologies
E - Ability to learn
OF 11) To be able to read independently scientific texts and articles in order to elaborate on the topics introduced in the course.

Educational objectives

GENERAL OBJECTIVES:
The course is an advanced module aimed at guiding the students through a journey at the boundary between statistical physics and machine learning by introducing advanced concepts of equilibrium and out of equilibrium statistical mechanics and by illustrating their applications to learning models and development of artificial intelligence.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) To acquire the main methods of statistical mechanics, probability and information theory relevant to applications in machine learning and inference, such as the replica approach, message passing, mutual information, data compression, Bayesian approaches
OF 2) To understand the different physical behaviour shown by inference and artificial learning procedures (curse of dimensionality, metastability, presence of multiple thermodynamic states)
B - Application skills
OF 3) To know how to apply an analytical technique to a given inference or learning setting to study its physical behavior
C - Autonomy of judgment
OF 4) Be able to recognize to which class of disordered systems a given inference or learning setting belongs
D - Communication skills
OF 5) Ability to learn from oral presentation of research results on topics similar to those introduced during the course
OF 6) Ability to present the course topics orally in a non-technical language that allows understanding even by those who have not yet taken the course
E - Ability to learn
OF 7) To be able to read scientific texts and articles in order to independently investigate the topics introduced during the course

Educational objectives

General objective
The objective of this course is to acquire an advanced theoretical-practical preparation aimed at understanding, analysing and managing the risks of degradation induced by climatic factors on indoor and outdoor materials, through the use of scientific methodologies, analytical tools and international regulatory references.

A - Knowledge and understanding
OF 1) To define and describe the fundamental climate variables in the field of the conservation of materials in indoor and outdoor environments
OF 2) To acquire knowledge on climate-induced degradation risks in indoor and outdoor environments
OF 3) To acquire knowledge on international regulations concerning climate-induced risks
B - Application skills
OF 4) To be able to apply methodological and instrumental procedures
OF 5) To be able to apply simplified functions
OF 6) To be able to apply international regulations on climate-induced risks
C - Autonomy of judgment
OF 7) To be able to interpret experimental and modelled data
OF 8) To be able to apply a scientific approach to conservation of built enviroment
OF 9) To be able to identify climate-induced degradation risks in indoor and outdoor environments
OF 10) To transfer scientific outcomes to the application of international regulations
D - Communication skills
OF 10) To know how to communicate scientific results
OF 11) To communicate the outputs of the analysis/study in clear way to the stakeholders keeping the scientific credibility
E - Ability to learn
OF 12) Have the ability to consult scientific literature to improve some of the topics covered during the course

Educational objectives

GENERAL OBJECTIVES:
The course aims to provide students with both theoretical and practical understanding of the main ground-based methods for atmospheric observation, with particular focus on the study of atmospheric aerosols, their interactions with electromagnetic radiation, and the use of scientific instrumentation for environmental monitoring.
SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) Knowledge and understanding of atmospheric processes and how they relate to the laws of classical physics applied to the atmosphere.
OF 2) Understanding the nature, origin, and role of atmospheric aerosols in climate and radiative processes.
OF 3) Understanding the physical principles underlying ground-based atmospheric remote sensing, with particular reference to LIDAR techniques.
OF 4) Understanding the physical processes involved in the interaction between electromagnetic radiation and the atmosphere.
B - Application skills
OF 5) Proper and safe use of basic instrumentation found in an atmospheric physics laboratory.
OF 6) Design and assembly of simple measurement systems, such as a telescope, for aerosol detection.
OF 7) Application of theoretical knowledge to carry out experimental measurements and interpret collected data in the context of aerosol optical properties.
OF 8) Use of computational tools and data analysis techniques to process and present the results of experimental observations.
C - Autonomy of judgment
OF 9) Ability to integrate the acquired knowledge in order to apply it within the broader context of atmospheric physics.
D - Communication skills
OF 10) Familiarity with the technical terminology of atmospheric physics.
E - Ability to learn
OF 11) Ability to consult scientific articles in order to independently explore topics introduced during the course.
OF 12) Ability to use open-source software available online to download atmospheric data and generate plots.

Educational objectives

GENERAL OBJECTIVES
The course “Advanced Computational Methods for Medical Physics” aims to provide the necessary knowledge on the computational techniques that are most used in the field of physics applied to medicine. In particular, the techniques currently used for "computational neuroimaging" will be discussed, that is, for the analysis of images obtained in the context of medical diagnostics, and the advanced simulation techniques with the Monte Carlo method for radiotherapy and neuroimaging. Practical investigation experiences in these fields will be proposed. At the end of the course, students will develop reasoning skills and quantitative resolution abilities useful for understanding and applying the aforementioned techniques.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) Know the fundamentals of the different computational neuroimaging techniques and of the Monte Carlo method applied to medical diagnostics;
OF 2) Understand the operating principles of the computational techniques involved;

B – Application skills
OF 3) Learn to choose the most advantageous computational technique for a given medical physics purpose;
OF 4) Understand the complementarity between the various computational techniques;

C - Autonomy of judgment
OF 5) Be able to integrate the knowledge acquired in order to apply it subsequently in the more general context of medical physics;

D – Communication skills
OF 6) Know how to communicate the basic concepts of the different computational techniques and the results potentially obtainable in the various fields;

E - Learning skills
OF 7) Have the ability to independently consult basic texts and scientific articles in order to independently study some topics introduced during the course.

Educational objectives

GENERAL OBJECTIVES
The course “Advanced Optical Techniques and Applications” aims to provide the necessary knowledge on optical and photonic techniques that are most used in the field of applied physics. In particular, the sources of electromagnetic radiation, photonic components and devices and spectrometers most used in optical and photonic investigation techniques in the biomedical field, in cultural heritage, in image analysis, in industrial processes, in photovoltaics and in the chemical-physical analysis, will be discussed. Practical investigation experiences in these fields will be proposed in some laboratories of the department. At the end of the course, students will develop reasoning skills and quantitative resolution abilities useful for understanding and applying the optical and photonic techniques most used in the various fields of applied physics.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) Know the fundamentals of different photonic and optical techniques and their use in the various fields of applied physics;
OF 2) Understand the principles of interaction between radiation and matter and the use of specific electromagnetic sources;
OF 3) Understand the functioning of various photonic devices, various spectrometers and various spectroscopy and microscopy techniques;

B - Application skills
OF 4) Learn to choose the most advantageous photonic and/or optical technique for specific applications;
OF 5) Understand the complementarity between the various optical and photonic techniques;
OF 6) Be able to understand the potential and experimental limitations of the various techniques considered;

C - Autonomy of judgment
OF 7) Be able to integrate the knowledge acquired in order to apply it subsequently in the more general context of applied physics;

D – Communication skills
OF 8) Know how to communicate the basic concepts of the different photonic and optical techniques and the results potentially obtainable in the various fields;

E - Learning ability
OF 9) Have the ability to independently consult basic texts and scientific articles in order to independently study some topics introduced during the course.

Educational objectives

GENERAL OBJECTIVES:
The course of Computational Statistical Mechanics aims to provide the necessary knowledge to understand and implement classical molecular dynamics and Monte Carlo techniques. The methods, that allow us to generate trajectories in phase space for sampling distinct statistical ensembles, will be studied. Some techniques which offer the possibility to calculate the free energy will be also discussed and it will be shown how the use of such results can provide a description of the atoms and molecules phase diagrams. At the end of the course, students will develop the ability of a quantitative reasoning and numerical skills useful for studying, modeling and understanding a large class of atomic and molecular systems as well as supramolecular aggregates. In addition, the student will be able to utilize the most common simulation packages which are available for a numerical study of complex systems, such as colloidal and bio-molecular systems, due to the acquired full knowledge of algorithms and numerical techniques on which these programs are built. Particular emphasis will be given to object-oriented and generic programming in the implementation of a computer simulation code. In particular, the modern C++ programming language will be introduced and discussed in the context of atomistic simulations. It will be also illustrated the use of the Python language, through the NumPy and MatPlotLib libraries, to analyze and visualize the data produced by computer simulations. During the course there will be also hands-on lectures, so that students will be able to put into practice the acquired knowledge through the implementation of their own simulation code. Students will be also stimulated to present the results obtained from the simulations, so as to test their ability to communicate clearly and effectively such results. The development of a numerical simulation code will be an opportunity for the students to design and develop their own project. This way they will be able to show their learning level and ability to apply independently the theoretical concepts acquired in the course.

SPECIFIC OBJECTIVES:

A - Knowledge and understanding
OF 1) Know common techniques to carry out computer simulations
OF 2) Know object oriented programming for scientific computations.
OF 3) Know common methods for analyzing data obtained from computer simulations.
OF 4) Understand data produced by computer simulations.

B - Application skills
OF 5) Ability to implement a simulation code.
OF 6) Ability to exploit simulations to obtain information about the physical properties of investigated systems.
OF 7) Be able to develop computer codes for analyzing data produced by computer simulations.

C - Autonomy of judgment
OF 8) Be able to critically analyze the results of “numerical experiments”.
OF 9) Be able to integrate autonomously the acquired knowledge in order to face new problems that require additional numeric techniques.
OF 10) Be able to identify the best technique to solve and study a physical problem numerically.

D - Communication skills
OF 11) Know how to communicate clearly to specialists and non-specialists, through manuscripts and presentations, the results obtained.
OF 12) Know how to clearly discuss a scientific topic.
OF 13) Know how to reproduce calculations related to a given scientific topic in a critical and informed manner.
E - Ability to learn
OF 14) Have the ability to learn new algorithms and numerical techniques by exploiting the scientific literature.
OF 15) Be able to conceive and develop their own project consisting of writing a simulation code or implementing a numerical technique.
OF 16) Be able to overcome difficulties and setbacks in the implementation of numerical techniques through original ideas and solutions.

Educational objectives

GENERAL OBJECTIVES:
The aim of the course 'Computational Solid State Physics' is to provide both theoretical and practical understanding with the two main numerical approaches currently in use for the solution of the quantum many body problem in condensed matter physics:

a) Density Functional Theory, which allows to obtain predictions from first principles of electronic states, structural energies, and interatomic forces in molecules and solids;
b) Quantum Monte Carlo methods - variational, diffusion, path-integral – which can be applied to the numerical study of various many-body quantum systems (liquid or solid helium, electron gas, electrons in atoms and molecules).

SPECIFIC OBJECTIVES:
A- Knowledge and Understanding:
OF1: To know and understand the fundamentals of Hartree-Fock (H-F) theory.
OF2: To know and understand the fundamentals of Density Functional Theory (DFT).
OF3: To know and understand the fundamentals of Pseudopotential theory (PPT).
OF4: To know and understand the DFT+PPT theory of crystalline systems.
OF5: To know and understand the variational Monte Carlo (MC) method for identical particles.
OF6: To know and understand the "projection MC" method for identical particles.
OF7: To know and understand the path integral Monte Carlo (PIMC) method.
OF8: To know and understand the "sign problem" for systems of many identical fermions.
B- Application Skills:
OF9: To apply DFT+PPT to simple solid-state systems (using software like Quantum Espresso).
OF10: To apply various quantum Monte Carlo methods to simple systems of many identical bosons or fermions (writing simple C codes and using large pre-existing FORTRAN codes).
C- Autonomy of Judgement:
OF11: To be able to assess, for a real quantum solid or fluid, which theories and algorithms presented in the course are suitable for describing and/or predicting which physical properties.
OF12: To be able to evaluate the feasibility, in terms of memory and CPU time, of a numerical project in molecular or solid-state physics.
D- Communication Skills:
OF13: To be able to present the results of a theoretical-numerical project.
OF14: To be able to write concise reports on the results of a theoretical-numerical project.
Ability to Learn:
OF15: To progress autonomously in C programming skills.
OF16: To progress autonomously in the use of existing software and codes.
OF17: To progress in graphical visualization skills of one's own results.
OF18: To progress in the ability to read reviews and research articles.

Educational objectives

GENERAL OBJECTIVES:
This course is designed as an introduction to computational biology and biophysics. It aims to bridge the gap between institutional learning and active research. The course is structured around three main aspects: i) TOPICS (principles, ideas); ii) METHODS (algorithms and computational techniques); iii) PERSPECTIVES of contemporary computational biology. Extensive reference and critical introductions to literature and current texts will be provided as guides for individual study. Efforts will be made to provide a clear framework of bibliographic references for each topic discussed, aiding in preparation for the final exam. At the end of the course, special guests will present original research lines of interest to students in biosystems, materials physics, and theoretical courses. By successfully completing the course, students will be able to navigate the world of computational biophysics at various scales (from molecules to cells) and master the main computation and analysis algorithms used in the field.

SPECIFIC OBJECTIVES:
A - Knowledge and Understanding
SO 1) Gain a historical-critical perspective of modern computational biology/biophysics
SO 2) Understand the fundamentals of modern evolutionary theory
SO 3) Gain practical experience with data analysis models based on Bayesian inference
SO 4) Gain direct experience with major bioinformatics databases (SwissProt, pFam, PDB,…)

B - Applied Skills
SO 7) Translate at least the main computational biophysics simulation and analysis algorithms into pseudo-code
SO 8) Improve programming skills in scripting languages (Python) or compiled languages (C/C++)
SO 9) Execute a molecular dynamics simulation of a small protein on GROMACS

C - Judgment Autonomy
SO 10) Evaluate the quality of a scientific article

D - Communication Skills
SO 11) Report the results of a research project to the class participants
SO 12) Actively participate in classroom discussions (in Italian and/or English)

E - Learning Skills
SO 13) Acquire fluency in consulting specific databases (e.g., PubMed, Google Scholar) to support/refute a research hypothesis
SO 14) Actively participate in the organization of self-learning groups

Educational objectives

GENERAL OBJECTIVES:
Acquire familiarity with advanced deep learning techniques based on differentiable neural network models with supervised, unsupervised and reinforced learning paradigms; acquire skills in modelling complex problems through deep learning techniques, and be able to apply them to different application contexts in the fields of physics and basic and applied scientific research.

Discussed topics include: general machine learning concepts, differentiable neural networks, regularization techniques. Convolutional neural network, neural network for sequence analysis (RNN, LSTM / GRU, Transformers). Advanced learning techniques: transfer learning, domain adaptation, adversarial learning, self-supervised and contrastive learning, model distillation.
Graph Neural Networks (static and dynamic) and application to structured models for physics: dynamic models, simulation of complex fluids, GNN Hamiltonians and Lagrangians. Generative and variational models: variational mean-field theory, expectation maximization, energy based and maximum entropy models (Hopfield networks, Boltzman machines and RBM), AutoEncoders, Variational AutoEncoders, GANs, Autoregressive flow models, invertible networks, generative models based on GNN. Quantum Neural Networks.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) Knowledge of the functioning of neural networks and their mathematical interpretation as universal approximators
OF 2) Understanding of the limits and potential of advanced machine learning models
OF 3) Understanding of the limits and potential of DL in solving physics problems

B - Application skills
OF 4) Design, implementation, commissioning and analysis of deep learning architectures to solve complex problems in physics and scientific research.

C - Autonomy of judgment
OF 5) To be able to evaluate the performance of different architectures, and to evaluate the generalization capacity of the same

D - Communication skills
OF 6) Being able to clearly communicate the formulation of an advanced learning problem and its implementation, its applicability in realistic contexts
OF 7) Being able to motivate and to evaluate the generalization capacity of a DL model

E - Ability to learn
OF 8) Being able to learn alternative and more complex techniques
OF 9) Being able to implement existing techniques in an efficient, robust and reliable manner

Educational objectives

This course analyzes the theory of phase transitions and of critical
phenomena. We develop in detail the theory of the Renormalization
Group of statistical systems, both with regard to the so-called
renormalization group in real space and to the one in momentum
space. The course will lead to an awareness of the general ideas that
are the basis of the theory of phase transitions and to a mastery of
the detailed techniques that allow for the development of the
necessary calculations.

Educational objectives

GENERAL OBJECTIVES:
The course in Physics of Liquids aims to provide the necessary knowledge
to understand the disordered state of matter. Emphasis will be directed toward the
connection between the inter-particle interaction potential and the resulting
equilibrium structure. The themes of short-range ordering
and of the dynamics in the fluid and glass phases
will be studied in depth. At the end of the course, students will develop quantitative reasoning skills and analytical abilities useful for studying, modelling and understanding phenomena related to disordered soft matter.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) To know the theory of classical fluids, from mean field models, to integral theories and perturbative approaches.
OF 2) To understand the physical basis of the integral closures.
OF 3) To know how to extract structural and dynamical quantities from the scattering of X rays and neutrons.
OF 4) Know how to go from a microscopic theory to a hydrodynamic theory.
B - Application skills
OF 5) To be able to compute the cluster integrals that compose the virial coefficient for simple interaction potentials.
OF 6) To be able to solve the equations governing the structure of a fluid in the presence of external fields.
OF 7) To be able to apply perturbative techniques
…
C - Autonomy of judgment
OF 8) To be able to understand the results of experiments and simualtions on simple and complex liquids.
OF 9) To be able to integrate the knowledge acquired in order to choose the best closure relations for a particular problem.
D - Communication skills
OF 10) To know how to communicate the results of experiments and simulations on simple liquids.

E - Ability to learn
OF 11) Have the ability to consult and understand books and articles in order to gain a deeper knowledge of the topics discussed during the course.

Educational objectives

GENERAL OBJECTIVES: The "Soft and Biological Matter" course aims to provide the necessary knowledge to understand the structure of soft and biological matter, in the relevant scales of
length and time. Important arguments include the origins of the effective forces between macromolecules, the aggregation processes which result in the formation of vesicles, micelles, membranes, the formation of gel phases, structural and dynamic properties of synthetic and biological (nucleic acids and proteins) polymers. At the end of the course, students will develop quantitative reasoning and analytical skills useful for studying, modelling and understanding phenomena related to the dynamic and structural properties of soft and biological matter.
SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) To understand the physics of soft and biological matter
OF 2) To understand energetic and entropic forces
OF 3) To understand molecular aggregation
OF 4) To understand thermodynamic stability and critical phenomena in soft matter
B - Application skills
OF5) To be able to apply learned methods/techniques to novel problems
C - Autonomy of judgment
OF 6) To be able to apply the topic discussed in the course to the general context of soft and biological matter.
D - Communication skills
E - Ability to learn
OF 7) To be able to understand a scientific publication and deepen her/his own understanding of the arguments discussed in the course.

Educational objectives

The student will acquire knowledge of the fundamental principles of light-matter interaction studied via semi-classical and quantum approaches. Moreover, the student will study different aspects related to the quantum mechanical nature of light and its characterization according to photon statistics. During the course, the student will also deal with non-linear optics and will study some practical applications of quantum optics.
A - Knowledge and understanding
OF 1) To understand the fundamentals of quantum optics and non linear optics.
OF 3) To understand phenomena related to light-matter interaction, using both semi-classical and quantum approaches.
B - Application skills
OF 4) To be able to use semi-classical and quantum approaches to understand phenomena related to the interaction of light with matter.
OF 5) To be able to apply the basic principles of quantum optics to solve simple problems related to the knowledge acquired during the course.
C - Autonomy of judgment
OF 6) To be able to evaluate which optical phenomena require a classical or quantum treatment of the electromagnetic field to be explained.
OF 7) To develop quantitative reasoning abilities and problem-solving skills, which represent the basis to study, model and understand quantum phenomena related to light-matter interaction.
D - Communication skills
OF 8) To know how to communicate the knowledge acquired during the course via presentation of a scientific work related to one particular topic discussed during the lecture.
E - Ability to learn
OF 9) Have the ability to consult scientific papers in the field of quantum optics.
OF 10) Have the ability to understand practical applications that use the basic principles of quantum optics.

Educational objectives

GENERAL OBJECTIVES:
Provide fundamental notions of: ultrashort pulses generation and propagation in linear and non-linear media, characterization of time and frequency, spatial and polarization profiles. Pinpoint selected examples of ultrafast processes in physics, chemistry and biology (molecular switches, photoreceptors isomerization, photoinduced processes in
hemeproteins). Highlight novel approaches to non linear imaging and
related instrumentation. Hands on laboratory tutorials.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) To know photonics foundations and its most common application
OF 2) To understand non linear processes relevant for propagation of light pulses in materials
OF 3) Understand principles of non-linear spectroscopy illustrated by Feynman diagrams

B - Application skills
OF 4) Learn how to apply equations for linear and non linear propagation to real cases such as short pulses in optical fibers.
OF 5) Solve problems related to evaluation of cross sections for linear and non linear spectroscopies
OF 6) To be able to apply numerical techniques for the evaluation of radiation – matter interaction

C - Autonomy of judgment
OF 7) To be able to apply in the future the acquired skills to complex problems in photochemistry and photobiology

D - Communication skills
OF 8) To know how to communicate the critical steps necessary to solve elementary problems dealing with spectroscopy and light matter interaction in non linear regime

E - Ability to learn
OF 9) Have the ability to autonomously consult scientific articles to expand the knowledge developed in the course

Educational objectives

GENERAL OBJECTIVES:
The course in Physics of Liquids aims to provide the necessary knowledge
to understand the disordered state of matter. Emphasis will be directed toward the
connection between the inter-particle interaction potential and the resulting
equilibrium structure. The themes of short-range ordering
and of the dynamics in the fluid and glass phases
will be studied in depth. At the end of the course, students will develop quantitative reasoning skills and analytical abilities useful for studying, modelling and understanding phenomena related to disordered soft matter.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) To know the theory of classical fluids, from mean field models, to integral theories and perturbative approaches.
OF 2) To understand the physical basis of the integral closures.
OF 3) To know how to extract structural and dynamical quantities from the scattering of X rays and neutrons.
OF 4) Know how to go from a microscopic theory to a hydrodynamic theory.
B - Application skills
OF 5) To be able to compute the cluster integrals that compose the virial coefficient for simple interaction potentials.
OF 6) To be able to solve the equations governing the structure of a fluid in the presence of external fields.
OF 7) To be able to apply perturbative techniques
…
C - Autonomy of judgment
OF 8) To be able to understand the results of experiments and simualtions on simple and complex liquids.
OF 9) To be able to integrate the knowledge acquired in order to choose the best closure relations for a particular problem.
D - Communication skills
OF 10) To know how to communicate the results of experiments and simulations on simple liquids.

E - Ability to learn
OF 11) Have the ability to consult and understand books and articles in order to gain a deeper knowledge of the topics discussed during the course.

Educational objectives

GENERAL OBJECTIVES:
Nanophotonics and Spectroscopic Methods" course aims to provide the necessary knowledge on spectroscopic and nanophotonics techniques in condensed matter to understand the characteristics of materials from the point of view of electronic, reticular and vibrational degrees of freedom both at equilibrium and out of equilibrium. Different spectroscopic techniques: neutron scattering, scattering and absorption of electromagnetic radiation, will be studied within the formalism of the scattering matrix S and the linear response theorem. It will be understood how from these techniques it is possible to study the spectrum of fundamental excitations in condensed matter such as the phonon spectrum, the electronic absorption of free particles, the effects of the superconductive transition in electromagnetic properties, the vibrational transitions in liquids and biophysical systems. At the end of the course, students will develop quantitative reasoning skills and analytical resolution skills useful for studying, modeling and understanding phenomena related to the electronic and vibrational properties of condensed m

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) Know the fundamentals of the different spectroscopies in the linear response
OF 2) To understand how to obtain the spectrum of the relevant excitations of dense and diliut liquids and crystalline solides.
OF 3) Understanding the principles of the interaction between radiation and matter neutrons matter

B - Application skills
OF 4) Learn how to choose the most advantageous spectroscopic technique for the study of specific condensed matter problems
OF 5) Understanding the complementarity between spectroscopic techniques
OF 6) Be able to understand the potential and experimental limitations of the various techniques considered

C - Autonomy of judgment
OF 7) To be able to apply in the future the acquired skills to the more general context of condensed matter physics

D - Communication skills
OF 8) Knowing how to communicate the basic concepts of the different spectroscopic techniques and the results potentially obtainable in the various fields.

E - Ability to learn
OF 10) Have the ability to autonomously consult basic textbooks and in some cases scientific articles to expand the knowledge developed in the course

Educational objectives

GENERAL OBJECTIVES

The bacterial cell occupies the same special place in biological physics as the hydrogen atom does in condensed matter physics, and for the same reasons. Bacteria are the first "atoms" of life to appear in the known Universe, and everything fundamental in life is found in bacteria, in its simplest forms. The aim of the course is to investigate some fundamental aspects of living systems in a journey that starts from the internal mechanisms by which the bacterial cell "thinks" and acts, passing through how the individual cell moves in the external physical environment and ending with the study of the collective behaviour of bacterial colonies.
All topics covered in the course are based on recent literature and discuss both experimental aspects and theoretical modelling.

SPECIFIC OBJECTIVES

A - Knowledge and understanding
OF 1) To know and understand the fundamentals of gene regulation in prokaryotes and the dynamics of transcriptional networks.
OF 2) To know and understand the fundamentals of low Reynolds number fluid dynamics.
OF 3) To know and understand the main manifestations of the out of equilibrium nature of active matter.

B - Application skills
OF 4) To be able to discuss the dynamical behaviour of a transcriptional network.
OF 5) Tp be able to solve some elementary problems of low Reynolds hydrodynamics.
OF 6) Tp be able to model the stochastic dynamics of active particle systems.
OF 7) To be able to describe with continuous models the growth of bacterial colonies.

C - Autonomy of judgement
OF 8) Using the knowledge acquired, the student will be able to formulate new models capable of describing situations not covered in the course.

D - Communication skills
OF 9) To know how to communicate in written reports an advanced concept.
OF 10) To be able to present a recent line of research in biophysics.

E - Ability to learn
OF 11) To be able to read independently scientific texts and articles in order to elaborate on the topics introduced in the course.

Educational objectives

Formative targets:

The objectives of the course are to bring the student to a deep knowledge and understanding of the basic mathematical properties i) of the nonlinear wave propagation with or without dispersion or dissipation; ii) of the construction of nonlinear mathematical models of physical interest, through the multiscale method, like the soliton equations, and of the mathematical techniques to solve them, arriving to the introduction of current research topics in the theory of solitons and anomalous waves. At the end of the course the student must be able i) to apply the acquired methods to problems in nonlinear physics even different from those studied in the course, in fluid dynamics, nonlinear optics, theory of gravitation, etc .., solving typical problems of the nonlinear dynamics; ii) to integrate in autonomy the acquired knowledges through the suggested literature, to solve also problems of interest for him/her, and not investigated in the course. The student will have the ability to consult supplementary material, interesting scientific papers, having acquired the right knowledges and critical skill to evaluate their content and their potential benefits to his/her scientific interests. At last the student must be able to conceive and develop a research project in autonomy. In order to achieve these goals, we plan to involve the student, during the theoretical lectures and exercises, through general and specific questions related to the subject; or through the presentation in depth of some specific subject agreed with the teacher.

Educational objectives

A - Knowledge and understanding
OF 1) To possess a basic knowledge of complexity science, i.e. the collective properties that emerge with a large number of interacting components (atoms, particles or bacteria in a physical or biological context, or people, machines or businesses in a socio-economic context).
OF 2) Understanding the mechanisms underlying the emergence of complex macroscopic properties from knowledge of microscopic mechanisms.
OF 3) Mastering the basic toolbox of a complexity scientist: information theory, network theory, scale invariance and critical phenomena, properties of dynamical systems, agent models.
B - Application skills
OF 4) Knowing how to devise simple models for complex phenomenologies.
OF 5) Being able to tackle complex problems analytically or computationally, translating research questions into concrete solution and verification actions.
OF 6) Being able to apply the techniques and methods learnt also outside the areas covered in the course.
OF 7) Integrating the knowledge acquired in order to formalise problems and obtain results and predictions of increasing accuracy.
C - Autonomy of judgment
OF 8) Being able to analyse phenomena, also through the acquisition of data and evidence, that fall within the scope of complexity and identify their essential elements.
OF 9) Being able to synthesise phenomenologies in order to be able to distill relevant and relevant questions.
OF 10) Being able to identify interesting new research directions.
D - Communication skills
OF 11) Being able to communicate complex issues in a simple way, focusing on the essential elements and revealing cause-effect relationships as far as possible.
OF 12) Being able to organise a coherent, profound yet comprehensible presentation.
OF 13) Knowing how to express one's thoughts in a way that stimulates group work and interaction with colleagues.
E - Ability to learn
OF 14) Have the ability to consult reference texts and articles.
OF 15) Being able to assess the relevance of results, their place in the scientific panorama of reference and their potential importance for the research topics of interest.
OF 16) Being able to design and develop a research project, identifying the main objectives and the possible paths to reach them.

Educational objectives

GENERAL OBJECTIVES:
This course is designed as an introduction to computational biology and biophysics. It aims to bridge the gap between institutional learning and active research. The course is structured around three main aspects: i) TOPICS (principles, ideas); ii) METHODS (algorithms and computational techniques); iii) PERSPECTIVES of contemporary computational biology. Extensive reference and critical introductions to literature and current texts will be provided as guides for individual study. Efforts will be made to provide a clear framework of bibliographic references for each topic discussed, aiding in preparation for the final exam. At the end of the course, special guests will present original research lines of interest to students in biosystems, materials physics, and theoretical courses. By successfully completing the course, students will be able to navigate the world of computational biophysics at various scales (from molecules to cells) and master the main computation and analysis algorithms used in the field.

SPECIFIC OBJECTIVES:
A - Knowledge and Understanding
SO 1) Gain a historical-critical perspective of modern computational biology/biophysics
SO 2) Understand the fundamentals of modern evolutionary theory
SO 3) Gain practical experience with data analysis models based on Bayesian inference
SO 4) Gain direct experience with major bioinformatics databases (SwissProt, pFam, PDB,…)

B - Applied Skills
SO 7) Translate at least the main computational biophysics simulation and analysis algorithms into pseudo-code
SO 8) Improve programming skills in scripting languages (Python) or compiled languages (C/C++)
SO 9) Execute a molecular dynamics simulation of a small protein on GROMACS

C - Judgment Autonomy
SO 10) Evaluate the quality of a scientific article

D - Communication Skills
SO 11) Report the results of a research project to the class participants
SO 12) Actively participate in classroom discussions (in Italian and/or English)

E - Learning Skills
SO 13) Acquire fluency in consulting specific databases (e.g., PubMed, Google Scholar) to support/refute a research hypothesis
SO 14) Actively participate in the organization of self-learning groups

Educational objectives

The student will acquire knowledge of the fundamental principles of light-matter interaction studied via semi-classical and quantum approaches. Moreover, the student will study different aspects related to the quantum mechanical nature of light and its characterization according to photon statistics. During the course, the student will also deal with non-linear optics and will study some practical applications of quantum optics.
A - Knowledge and understanding
OF 1) To understand the fundamentals of quantum optics and non linear optics.
OF 3) To understand phenomena related to light-matter interaction, using both semi-classical and quantum approaches.
B - Application skills
OF 4) To be able to use semi-classical and quantum approaches to understand phenomena related to the interaction of light with matter.
OF 5) To be able to apply the basic principles of quantum optics to solve simple problems related to the knowledge acquired during the course.
C - Autonomy of judgment
OF 6) To be able to evaluate which optical phenomena require a classical or quantum treatment of the electromagnetic field to be explained.
OF 7) To develop quantitative reasoning abilities and problem-solving skills, which represent the basis to study, model and understand quantum phenomena related to light-matter interaction.
D - Communication skills
OF 8) To know how to communicate the knowledge acquired during the course via presentation of a scientific work related to one particular topic discussed during the lecture.
E - Ability to learn
OF 9) Have the ability to consult scientific papers in the field of quantum optics.
OF 10) Have the ability to understand practical applications that use the basic principles of quantum optics.

Educational objectives

GENERAL OBJECTIVES: The "Soft and Biological Matter" course aims to provide the necessary knowledge to understand the structure of soft and biological matter, in the relevant scales of
length and time. Important arguments include the origins of the effective forces between macromolecules, the aggregation processes which result in the formation of vesicles, micelles, membranes, the formation of gel phases, structural and dynamic properties of synthetic and biological (nucleic acids and proteins) polymers. At the end of the course, students will develop quantitative reasoning and analytical skills useful for studying, modelling and understanding phenomena related to the dynamic and structural properties of soft and biological matter.
SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) To understand the physics of soft and biological matter
OF 2) To understand energetic and entropic forces
OF 3) To understand molecular aggregation
OF 4) To understand thermodynamic stability and critical phenomena in soft matter
B - Application skills
OF5) To be able to apply learned methods/techniques to novel problems
C - Autonomy of judgment
OF 6) To be able to apply the topic discussed in the course to the general context of soft and biological matter.
D - Communication skills
E - Ability to learn
OF 7) To be able to understand a scientific publication and deepen her/his own understanding of the arguments discussed in the course.

Educational objectives

This course analyzes the theory of phase transitions and of critical
phenomena. We develop in detail the theory of the Renormalization
Group of statistical systems, both with regard to the so-called
renormalization group in real space and to the one in momentum
space. The course will lead to an awareness of the general ideas that
are the basis of the theory of phase transitions and to a mastery of
the detailed techniques that allow for the development of the
necessary calculations.

Educational objectives

GENERAL OBJECTIVES:

The main goal of the course is to introduce students to the mathematical theory of groups (mainly: discrete groups and compact Lie groups) by a Mathematical Physics approach which emphasizes the role of representations of symmetries in terms of states or observables of the corresponding theory. Such an approach allows an immediate comparison between classical theories (Poisson brackets) and quantum theories (commutators).

SPECIFIC OBJECTIVES:

A - Knowledge and understanding
OF1) To know the fundamental concepts in the theory of finite groups and matrix Lie groups, and in the theory of their linear, unitary or projective representations.
OF2) To know the mathematical structure of the Lie groups which more often appear in physical theories, and to understand the relation between such groups and the symmetries of the physical theory.
OF3) To understand the role of symmetries and Lie groups in (relativistic) field theories.
OF4) To understand the mathematical language of differential forms, and the reformulation of electromagnetism in such a language.

B – Application skills
OF 5) To be able to compute the commutation relations among the generators of the Lie algebra of a given (matrix) Lie group; to be able to explicitly compute such commutation relations in the most relevant cases: the rotation group, the Poincaré group, and the group SU(3).
OF 6) To be able to compute the tensor product of two representations of the rotation group, by using the Wigner Eckart theorem; to be able to interpret the result of such a computation in the application to compound systems (e.g. molecules).
OF7) To be able to determine whether a given differential form is closed and/or exact; to be able to translate the concepts concerning differential forms in the analogous concepts of vector analysis (gradient, curl or rotational, divergence) and vice versa.

C - Autonomy of judgment
OF 8) To be able to critically read an advanced book on symmetries in physics.
OF 9) To be able to integrate the knowledge acquired within the course, in order to apply them in the context of different physical theories, in connection e.g. with high energy physics or with condensed matter physics.

D – Communication skills
OF 10) Ability to discuss the symmetries of a physical system by appropriately using the language of differential forms and Lie groups.

E - Ability to learn
OF 11) Ability to read advanced monographies and research papers, which usually use the mathematical language of Lie groups and differential forms.
OF 12) Ability to "construct" a physical theory, by implementing in the theory the symmetries of the physical system under investigation, using Lie algebras and Lie groups as a fundamental tool.

Educational objectives

GENERAL OBJECTIVES:
The course of Computational Statistical Mechanics aims to provide the necessary knowledge to understand and implement classical molecular dynamics and Monte Carlo techniques. The methods, that allow us to generate trajectories in phase space for sampling distinct statistical ensembles, will be studied. Some techniques which offer the possibility to calculate the free energy will be also discussed and it will be shown how the use of such results can provide a description of the atoms and molecules phase diagrams. At the end of the course, students will develop the ability of a quantitative reasoning and numerical skills useful for studying, modeling and understanding a large class of atomic and molecular systems as well as supramolecular aggregates. In addition, the student will be able to utilize the most common simulation packages which are available for a numerical study of complex systems, such as colloidal and bio-molecular systems, due to the acquired full knowledge of algorithms and numerical techniques on which these programs are built. Particular emphasis will be given to object-oriented and generic programming in the implementation of a computer simulation code. In particular, the modern C++ programming language will be introduced and discussed in the context of atomistic simulations. It will be also illustrated the use of the Python language, through the NumPy and MatPlotLib libraries, to analyze and visualize the data produced by computer simulations. During the course there will be also hands-on lectures, so that students will be able to put into practice the acquired knowledge through the implementation of their own simulation code. Students will be also stimulated to present the results obtained from the simulations, so as to test their ability to communicate clearly and effectively such results. The development of a numerical simulation code will be an opportunity for the students to design and develop their own project. This way they will be able to show their learning level and ability to apply independently the theoretical concepts acquired in the course.

SPECIFIC OBJECTIVES:

A - Knowledge and understanding
OF 1) Know common techniques to carry out computer simulations
OF 2) Know object oriented programming for scientific computations.
OF 3) Know common methods for analyzing data obtained from computer simulations.
OF 4) Understand data produced by computer simulations.

B - Application skills
OF 5) Ability to implement a simulation code.
OF 6) Ability to exploit simulations to obtain information about the physical properties of investigated systems.
OF 7) Be able to develop computer codes for analyzing data produced by computer simulations.

C - Autonomy of judgment
OF 8) Be able to critically analyze the results of “numerical experiments”.
OF 9) Be able to integrate autonomously the acquired knowledge in order to face new problems that require additional numeric techniques.
OF 10) Be able to identify the best technique to solve and study a physical problem numerically.

D - Communication skills
OF 11) Know how to communicate clearly to specialists and non-specialists, through manuscripts and presentations, the results obtained.
OF 12) Know how to clearly discuss a scientific topic.
OF 13) Know how to reproduce calculations related to a given scientific topic in a critical and informed manner.
E - Ability to learn
OF 14) Have the ability to learn new algorithms and numerical techniques by exploiting the scientific literature.
OF 15) Be able to conceive and develop their own project consisting of writing a simulation code or implementing a numerical technique.
OF 16) Be able to overcome difficulties and setbacks in the implementation of numerical techniques through original ideas and solutions.

Educational objectives

GENERAL OBJECTIVES:
The aim of the course 'Computational Solid State Physics' is to provide both theoretical and practical understanding with the two main numerical approaches currently in use for the solution of the quantum many body problem in condensed matter physics:

a) Density Functional Theory, which allows to obtain predictions from first principles of electronic states, structural energies, and interatomic forces in molecules and solids;
b) Quantum Monte Carlo methods - variational, diffusion, path-integral – which can be applied to the numerical study of various many-body quantum systems (liquid or solid helium, electron gas, electrons in atoms and molecules).

SPECIFIC OBJECTIVES:
A- Knowledge and Understanding:
OF1: To know and understand the fundamentals of Hartree-Fock (H-F) theory.
OF2: To know and understand the fundamentals of Density Functional Theory (DFT).
OF3: To know and understand the fundamentals of Pseudopotential theory (PPT).
OF4: To know and understand the DFT+PPT theory of crystalline systems.
OF5: To know and understand the variational Monte Carlo (MC) method for identical particles.
OF6: To know and understand the "projection MC" method for identical particles.
OF7: To know and understand the path integral Monte Carlo (PIMC) method.
OF8: To know and understand the "sign problem" for systems of many identical fermions.
B- Application Skills:
OF9: To apply DFT+PPT to simple solid-state systems (using software like Quantum Espresso).
OF10: To apply various quantum Monte Carlo methods to simple systems of many identical bosons or fermions (writing simple C codes and using large pre-existing FORTRAN codes).
C- Autonomy of Judgement:
OF11: To be able to assess, for a real quantum solid or fluid, which theories and algorithms presented in the course are suitable for describing and/or predicting which physical properties.
OF12: To be able to evaluate the feasibility, in terms of memory and CPU time, of a numerical project in molecular or solid-state physics.
D- Communication Skills:
OF13: To be able to present the results of a theoretical-numerical project.
OF14: To be able to write concise reports on the results of a theoretical-numerical project.
Ability to Learn:
OF15: To progress autonomously in C programming skills.
OF16: To progress autonomously in the use of existing software and codes.
OF17: To progress in graphical visualization skills of one's own results.
OF18: To progress in the ability to read reviews and research articles.

Educational objectives

GENERAL OBJECTIVES

The bacterial cell occupies the same special place in biological physics as the hydrogen atom does in condensed matter physics, and for the same reasons. Bacteria are the first "atoms" of life to appear in the known Universe, and everything fundamental in life is found in bacteria, in its simplest forms. The aim of the course is to investigate some fundamental aspects of living systems in a journey that starts from the internal mechanisms by which the bacterial cell "thinks" and acts, passing through how the individual cell moves in the external physical environment and ending with the study of the collective behaviour of bacterial colonies.
All topics covered in the course are based on recent literature and discuss both experimental aspects and theoretical modelling.

SPECIFIC OBJECTIVES

A - Knowledge and understanding
OF 1) To know and understand the fundamentals of gene regulation in prokaryotes and the dynamics of transcriptional networks.
OF 2) To know and understand the fundamentals of low Reynolds number fluid dynamics.
OF 3) To know and understand the main manifestations of the out of equilibrium nature of active matter.

B - Application skills
OF 4) To be able to discuss the dynamical behaviour of a transcriptional network.
OF 5) Tp be able to solve some elementary problems of low Reynolds hydrodynamics.
OF 6) Tp be able to model the stochastic dynamics of active particle systems.
OF 7) To be able to describe with continuous models the growth of bacterial colonies.

C - Autonomy of judgement
OF 8) Using the knowledge acquired, the student will be able to formulate new models capable of describing situations not covered in the course.

D - Communication skills
OF 9) To know how to communicate in written reports an advanced concept.
OF 10) To be able to present a recent line of research in biophysics.

E - Ability to learn
OF 11) To be able to read independently scientific texts and articles in order to elaborate on the topics introduced in the course.

Educational objectives

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) To know the elements of the computer hardware and software architecture and to understand their interactions.
OF 2) To know the techniques needed to develop optimized code for a given computer architecture.
OF 3) To know the fundamentals of logic design of digital circuits using hardware description languages (VHDL).

B - Application skills
OF 4) To be able to evaluate the execution performance of code on a given computer architecture.
OF 5) To be able to develop scientific code optimized for a given computer architecture.
OF 6) To be able to select the computer architecture best suited for a given application.
OF 7) To be able to implement a circuit through VHDL coding and to simulate its behaviour.
C - Autonomy of judgment
OF 8) To be able to integrate the knowledge acquired in order to apply them for the processing needs in the experimental or theoretical Physics.

D - Communication skills

E - Ability to learn
OF 9) Have the ability to follow up the development in computer architectures.

Educational objectives

GENERAL OBJECTIVES:
Acquire familiarity with advanced deep learning techniques based on differentiable neural network models with supervised, unsupervised and reinforced learning paradigms; acquire skills in modelling complex problems through deep learning techniques, and be able to apply them to different application contexts in the fields of physics and basic and applied scientific research.

Discussed topics include: general machine learning concepts, differentiable neural networks, regularization techniques. Convolutional neural network, neural network for sequence analysis (RNN, LSTM / GRU, Transformers). Advanced learning techniques: transfer learning, domain adaptation, adversarial learning, self-supervised and contrastive learning, model distillation.
Graph Neural Networks (static and dynamic) and application to structured models for physics: dynamic models, simulation of complex fluids, GNN Hamiltonians and Lagrangians. Generative and variational models: variational mean-field theory, expectation maximization, energy based and maximum entropy models (Hopfield networks, Boltzman machines and RBM), AutoEncoders, Variational AutoEncoders, GANs, Autoregressive flow models, invertible networks, generative models based on GNN. Quantum Neural Networks.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) Knowledge of the functioning of neural networks and their mathematical interpretation as universal approximators
OF 2) Understanding of the limits and potential of advanced machine learning models
OF 3) Understanding of the limits and potential of DL in solving physics problems

B - Application skills
OF 4) Design, implementation, commissioning and analysis of deep learning architectures to solve complex problems in physics and scientific research.

C - Autonomy of judgment
OF 5) To be able to evaluate the performance of different architectures, and to evaluate the generalization capacity of the same

D - Communication skills
OF 6) Being able to clearly communicate the formulation of an advanced learning problem and its implementation, its applicability in realistic contexts
OF 7) Being able to motivate and to evaluate the generalization capacity of a DL model

E - Ability to learn
OF 8) Being able to learn alternative and more complex techniques
OF 9) Being able to implement existing techniques in an efficient, robust and reliable manner

Educational objectives

General Objectives:
To acquire knowledge of fundamental topics in Mathematical Physics and the related mathematical methods.

Specific Objectives:

Knowledge and Understanding:

By the end of the course, students will be familiar with the fundamentals of operator theory in Hilbert spaces, the mathematical structure of quantum mechanics, and the basic methods for studying problems in quantum mechanics from the perspective of mathematical physics.

Applying knowledge and understanding:

Students who pass the exam will be able to: i) apply the results of operator theory, ii) construct self-adjoint Hamiltonians and study their spectra, iii) rigorously approach a scattering problem, iv) understand the mathematical methods required for the study of the dynamics of many-body systems, with particular regard to the phenomenon of condensation.

Critical Thinking and Judgment:

Students who pass the exam will be able to recognize a mathematical-physical approach and analyze similarities and differences compared to the typical approach in Theoretical Physics.

Communication Skills:

Students who pass the exam will have developed the ability to communicate concepts, ideas, and methodologies in mathematical physics.

Learning Skills:

The knowledge acquired will enable students to pursue further study—either independently or through other courses—on more specialized aspects of the methods of mathematical physics.

Educational objectives

A - Knowledge and understanding
OF 1) Starting from the study of neurobiology of the nervous system, the student will first concentrate on the mechanisms regulating the electro-chemical properties of nerve cells and their connections, eventually studing the dynamics of populations of neuronal networks. The knowledge acquired will be on nonlinear and statistical physics compared to experimental data.
OF 2) The students will develop generally applicable skills in the field of theoretical physics of the complex systems and the nonlinear dynamics.
B - Application skills
OF 3) The student will be able to understand the dynamics of neuronal populations at the basis of the cognitive functions like decision making and short-term memory.
OF 4) The student will be able to apply analysis techniques and methods to electrophysiological data.
C - Autonomy of judgment
OF 5) By attending the lessons and with the regular interaction during the lessons themselves, the student will develop adequate autonomy of judgment, as he/she will be able to interface constantly with the teacher and critically analyze the information learned.
D - Communication skills
OF 6) The skills on the neurobiology of the nervous system will allow the student to interact with environments different from physics, enabling him/her to initiate multidisciplinary interactions in the life sciences.
E - Ability to learn
OF 7) The student will have the ability to evaluate and solve various problems of both data analysis and physics of complex systems.
OF 8) The acquired knowledge will allow the student to tackle the study of interdisciplinary papers on the physical phenomena underlying the behavior of the nervous system.

Educational objectives

Formative targets:

The objectives of the course are to bring the student to a deep knowledge and understanding of the basic mathematical properties i) of the nonlinear wave propagation with or without dispersion or dissipation; ii) of the construction of nonlinear mathematical models of physical interest, through the multiscale method, like the soliton equations, and of the mathematical techniques to solve them, arriving to the introduction of current research topics in the theory of solitons and anomalous waves. At the end of the course the student must be able i) to apply the acquired methods to problems in nonlinear physics even different from those studied in the course, in fluid dynamics, nonlinear optics, theory of gravitation, etc .., solving typical problems of the nonlinear dynamics; ii) to integrate in autonomy the acquired knowledges through the suggested literature, to solve also problems of interest for him/her, and not investigated in the course. The student will have the ability to consult supplementary material, interesting scientific papers, having acquired the right knowledges and critical skill to evaluate their content and their potential benefits to his/her scientific interests. At last the student must be able to conceive and develop a research project in autonomy. In order to achieve these goals, we plan to involve the student, during the theoretical lectures and exercises, through general and specific questions related to the subject; or through the presentation in depth of some specific subject agreed with the teacher.

Educational objectives

GENERAL OBJECTIVES:
Provide fundamental notions of: ultrashort pulses generation and propagation in linear and non-linear media, characterization of time and frequency, spatial and polarization profiles. Pinpoint selected examples of ultrafast processes in physics, chemistry and biology (molecular switches, photoreceptors isomerization, photoinduced processes in
hemeproteins). Highlight novel approaches to non linear imaging and
related instrumentation. Hands on laboratory tutorials.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) To know photonics foundations and its most common application
OF 2) To understand non linear processes relevant for propagation of light pulses in materials
OF 3) Understand principles of non-linear spectroscopy illustrated by Feynman diagrams

B - Application skills
OF 4) Learn how to apply equations for linear and non linear propagation to real cases such as short pulses in optical fibers.
OF 5) Solve problems related to evaluation of cross sections for linear and non linear spectroscopies
OF 6) To be able to apply numerical techniques for the evaluation of radiation – matter interaction

C - Autonomy of judgment
OF 7) To be able to apply in the future the acquired skills to complex problems in photochemistry and photobiology

D - Communication skills
OF 8) To know how to communicate the critical steps necessary to solve elementary problems dealing with spectroscopy and light matter interaction in non linear regime

E - Ability to learn
OF 9) Have the ability to autonomously consult scientific articles to expand the knowledge developed in the course

Educational objectives

GENERAL OBJECTIVES:
The course in Physics of Liquids aims to provide the necessary knowledge
to understand the disordered state of matter. Emphasis will be directed toward the
connection between the inter-particle interaction potential and the resulting
equilibrium structure. The themes of short-range ordering
and of the dynamics in the fluid and glass phases
will be studied in depth. At the end of the course, students will develop quantitative reasoning skills and analytical abilities useful for studying, modelling and understanding phenomena related to disordered soft matter.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) To know the theory of classical fluids, from mean field models, to integral theories and perturbative approaches.
OF 2) To understand the physical basis of the integral closures.
OF 3) To know how to extract structural and dynamical quantities from the scattering of X rays and neutrons.
OF 4) Know how to go from a microscopic theory to a hydrodynamic theory.
B - Application skills
OF 5) To be able to compute the cluster integrals that compose the virial coefficient for simple interaction potentials.
OF 6) To be able to solve the equations governing the structure of a fluid in the presence of external fields.
OF 7) To be able to apply perturbative techniques
…
C - Autonomy of judgment
OF 8) To be able to understand the results of experiments and simualtions on simple and complex liquids.
OF 9) To be able to integrate the knowledge acquired in order to choose the best closure relations for a particular problem.
D - Communication skills
OF 10) To know how to communicate the results of experiments and simulations on simple liquids.

E - Ability to learn
OF 11) Have the ability to consult and understand books and articles in order to gain a deeper knowledge of the topics discussed during the course.

Educational objectives

GENERAL OBJECTIVES:
Nanophotonics and Spectroscopic Methods" course aims to provide the necessary knowledge on spectroscopic and nanophotonics techniques in condensed matter to understand the characteristics of materials from the point of view of electronic, reticular and vibrational degrees of freedom both at equilibrium and out of equilibrium. Different spectroscopic techniques: neutron scattering, scattering and absorption of electromagnetic radiation, will be studied within the formalism of the scattering matrix S and the linear response theorem. It will be understood how from these techniques it is possible to study the spectrum of fundamental excitations in condensed matter such as the phonon spectrum, the electronic absorption of free particles, the effects of the superconductive transition in electromagnetic properties, the vibrational transitions in liquids and biophysical systems. At the end of the course, students will develop quantitative reasoning skills and analytical resolution skills useful for studying, modeling and understanding phenomena related to the electronic and vibrational properties of condensed m

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) Know the fundamentals of the different spectroscopies in the linear response
OF 2) To understand how to obtain the spectrum of the relevant excitations of dense and diliut liquids and crystalline solides.
OF 3) Understanding the principles of the interaction between radiation and matter neutrons matter

B - Application skills
OF 4) Learn how to choose the most advantageous spectroscopic technique for the study of specific condensed matter problems
OF 5) Understanding the complementarity between spectroscopic techniques
OF 6) Be able to understand the potential and experimental limitations of the various techniques considered

C - Autonomy of judgment
OF 7) To be able to apply in the future the acquired skills to the more general context of condensed matter physics

D - Communication skills
OF 8) Knowing how to communicate the basic concepts of the different spectroscopic techniques and the results potentially obtainable in the various fields.

E - Ability to learn
OF 10) Have the ability to autonomously consult basic textbooks and in some cases scientific articles to expand the knowledge developed in the course

Educational objectives

GENERAL OBJECTIVES:
The main objective of the course in Theoretical Biophysics is to show how statistical physics has a crucial role for a quantitative understanding of many biological
phenomena. To this aim, the course focuses on two very general aspects present in a variety of biological processes: the role of noise and the signal to noise ratio; the
emergence of collective phenomena.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) To acquire some fundamental background in statistical physics, related in particular to elementary stochastic processes, critical phenomena and statistical inference
OF 2) To learn the phenomenology of several important biological processes such as chemotaxis and chemoreception, photoreception, proteins, neural networks, living active matter and collective motion.
OF 3) to acquire modeling techniques

B - Application skills
OF 4) To be able to apply theoretical concepts and models to the quantitative description of the phenomenology experimentally characterized. To build models starting from the data.

C - Autonomy of judgment
OF 5) To be able to modify approaches derived from statistical physics to study specific phenomena occurring in biological systems.

D - Communication skills

E - Ability to learn
OF 6) Have the ability to consult and study scientific texts and literature of both theoretical and experimental character in a highly interdisciplinary context.

Educational objectives

GENERAL OBJECTIVES:
The Molecular Biology course is designed to provide students the conceptual and methodological basis required to study the molecular mechanisms regulating gene expression in physiological and pathological conditions, including epigenetics. In addition to the knowledge on the structure and metabolism of nucleic acids, the course will introduce the most relevant techniques of DNA cloning, DNA and RNA manipulation and the applications of Genetic Engineering to basic research and biomedicine. Topics discussed will also include the recent generation of sequencing technologies in light of their importance for the recent annotation of emerging noncoding RNA genes. The discovery of long noncoding and circular RNAs will be also discussed as well as the in vivo approaches used to study their functional role (practical examples taken from recent literature will be used). The course will include lectures and seminars. By the end of the course, students will be able to apply the acquired knowledge to the study of the basic mechanisms of gene expression, as well as of complex processes such as development, cell division and differentiation, and to exploit them for a practical use in both basic and applied research.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) to know the mechanisms of regulation of gene expression and the technological methods available to intervene on it;
OF 2) to know the structure and function of the genome in humans and in the main model systems;
OF 3) to know the origin and the maintenance of the biological complexity;
OF 4) to understand the influence of the modern sequencing technologies for a better description and for the study of transcriptome dynamics in humans and in the main model systems;
OF 5) to understand the network of interactions between the biological molecules in the mechanisms of regulation of gene expression.

B - Application skills
OF 6) To be able to discriminate techniques to apply according to the different problems to be dealt with in the molecular biology field

C - Autonomy of judgment
OF 7) To be able to use the specific terminology;
OF 8) To be able to interpret the biological phenomena in a multi-scale and multi-factorial context;
OF 9) To be able to interpret the results of genomic studies

D - Communication skills
OF 10) To know how to report papers already present in the literature in the form of an oral presentation

E - Ability to learn
OF 11) Have the ability to search and consult the scientific literature in the main biological databases
OF 12) Have the ability to evaluate the importance and the stringency of the published data

Educational objectives

A - Knowledge and understanding
OF 1) To possess a basic knowledge of complexity science, i.e. the collective properties that emerge with a large number of interacting components (atoms, particles or bacteria in a physical or biological context, or people, machines or businesses in a socio-economic context).
OF 2) Understanding the mechanisms underlying the emergence of complex macroscopic properties from knowledge of microscopic mechanisms.
OF 3) Mastering the basic toolbox of a complexity scientist: information theory, network theory, scale invariance and critical phenomena, properties of dynamical systems, agent models.
B - Application skills
OF 4) Knowing how to devise simple models for complex phenomenologies.
OF 5) Being able to tackle complex problems analytically or computationally, translating research questions into concrete solution and verification actions.
OF 6) Being able to apply the techniques and methods learnt also outside the areas covered in the course.
OF 7) Integrating the knowledge acquired in order to formalise problems and obtain results and predictions of increasing accuracy.
C - Autonomy of judgment
OF 8) Being able to analyse phenomena, also through the acquisition of data and evidence, that fall within the scope of complexity and identify their essential elements.
OF 9) Being able to synthesise phenomenologies in order to be able to distill relevant and relevant questions.
OF 10) Being able to identify interesting new research directions.
D - Communication skills
OF 11) Being able to communicate complex issues in a simple way, focusing on the essential elements and revealing cause-effect relationships as far as possible.
OF 12) Being able to organise a coherent, profound yet comprehensible presentation.
OF 13) Knowing how to express one's thoughts in a way that stimulates group work and interaction with colleagues.
E - Ability to learn
OF 14) Have the ability to consult reference texts and articles.
OF 15) Being able to assess the relevance of results, their place in the scientific panorama of reference and their potential importance for the research topics of interest.
OF 16) Being able to design and develop a research project, identifying the main objectives and the possible paths to reach them.

Educational objectives

GENERAL OBJECTIVES:
The goal of the course is the study of the foundations of Quantum Field Theory, starting from thee quantization of the free fields up to the introduction of the interaction of the Dirac field with the electromagnetic field (QED) and to the definition and calculation of a cross section at tree-level in perturbation theory.
The student will acquire the basic concepts of the quantization of the fields and he will be able to apply the Feynman rules for the calculation of a cross section at tree-level.
The know-how that the student acquires attending this course is indispensable for the advanced courses in Quantum Field Theory, in particular for the curriculum in Particle and Astroparticle Physics.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) Knowing the basis of the theory of classical and quantum fields, Lagrangian and Hamiltonian description. To be able to discuss the symmetries of a physical system and, accordingly, the conserved quantities.
OF 2) Understanding the basis of the canonical quantization and its applications to the free and interacting fields. To understand the scattering matrix.
OF 3) Knowing the definition and the basis of the calculation of a cross section.
B - Application skills
OF 5) Knowing the Feynman rules for the interaction of the Dirac and Electromagnetic fields (QED) and to be able to theoretically predict a cross section for a QED process at the tree-level in peruturbation theory.
C - Autonomy of judgment
OF 8) To be able to integrate the knowledge acquired in order to apply it in the more general context of Quantum Field Theory, renormalization and general higher-orders calculations in perturbation theory.
D - Communication skills
OF 10) Ability to discuss about the quantum theory of fields with the appropriate rigor and understanding of the approximations used

E - Ability to learn
OF 11) To be able to read independently scientific texts and articles in order to elaborate on the topics introduced in the course.

Educational objectives

GENERAL OBJECTIVES:
Aim of the course is to introduce the basic notions of the modern theory of gravity, and of its more important conceptual and astrophysical implications.

At the end of the course the student should: 1) have acquired the instruments of differential geometry which allow to formulate Einstein's equations and derive its predictions. 2) Have understood what is the role of the equivalence principle between gravitational and inertial mass in the formulation of the theory, and why the gravitational field modifies the spacetime geometry. 3) Have understood how to use the symmetries of a physical problem to simplify Einstein's equations and find solutions. 4) Be able to derive the solution describing the gravitational field external to a
non rotating, spherically symmetric body (the Schwarzschild solution), and to show that this solution can also represent a non rotating black hole. 5) Have understood how some of the main predictions of General Relativity can be obtained by solving the geodesic equations, which describe the motion of free particles in a gravitational field. 6) Have understood how to solve Einstein's equations in the weak field limit, to show that spacetime perturbations propagate as gravitational
waves.

Therefore, at the end of the course the student should: 1) be able to compute how vectors, one-forms and tensors transform under a coordinate transformation; to compute the covariant derivative of these geometrical objects and to solve exercises which involve these operations in tensor equations. 2) Be able to compute how does a vector change when parallely transported along a path in curved spacetime, and to derive the curvature tensor using this operation. 3) Be able to derive Einstein's equations. 4) Be able to derive and interpret some of the most interesting predictions of General Relativity: the gravitational redshift, light deflection near massive bodies, precession of Mercury perihelion, existence of gravitational waves.