Relativistic astrophysics (Luigi Foschini, I e II anno)
summary: - Classical Relativity (Galilean) 
- Special Relativity (Minkowski spacetime, beaming, superluminal motion) 
- General Relativity (tensors) 
- Equations of the Gravitational Field and solutions of astrophysical interest (black holes, cosmology, gravitational waves) 
- Radiative Processes (bremsstrahlung, synchrotron, Compton scattering)
 - Accretion onto compact objects (types of accretion disk, corona and X-ray emission lines)
 - Outflows: winds and relativistic jets - Instruments and Data Analysis for high-energy astrophysics (hardware, software, calibration)
 - Hands-on examples of X-ray data analysis (data of Neil Gehrels Swift Observatory). Lecture notes will be available at due time (currently under revision).

Feynman path integrals (Phil Ratcliffe, I e II anno) 
This short lecture series provides a very brief introduction to the Feynman Path Integral approach to quantisation, which represents a completely original and alternative axiomatic basis for quantum theories. While developed within the framework of non-relativistic quantum mechanics, the method is of particular importance (for its clarity and simplicity) in second or field quantisation. However, it finds useful applications in many other areas, as diverse as statistical mechanics and even, for example, financial analysis. Being limited to eight hours of front-on lectures, little attention is paid to mathematical rigour. In other words, a description of the physical basis and significance will be provided, together with some of the interesting applications of the technique of relevance to physics.
 

Quantum Technologies (Alessia Allevi, Giuliano Benenti, Maria Bondani, I anno) 
The second quantum revolution is unfolding now, exploiting the enormous advancements in our ability to detect and manipulate single quantum objects and triggering the development of the different quantum technologies. The course, after a preliminary introduction to the principles of quantum information, is intended to give an introduction to the different quantum technologies for computing, simulation, communication, metrology, and machine learning, including quantum optics laboratory demonstration of quantum information protocols.

Introduction to non equilibrium statistical physics (Francesco Ginelli, II anno) 
Classical statistical mechanics describes system at thermodynamic equilibrium. However, a wide range of natural systems, ranging from climate to virtually all living matter, are kept out of equilibrium by external driving and/or fluxes of energy which is constantly absorbed and dissipated through the system. This course introduces some of the concepts employed in the study of macroscopic systems away from their state of thermodynamic equilibrium, mainly covering kinetic theory, stochastic processes and linear response. These constitute the principles to describe systems slightly perturbed out of equilibrium. Other selected topics may include active matter, pattern formation and systems with absorbing states.

Non-Newtonian aspects of general relativity (Sergio Cacciatori, II anno) 
This is a 20-hour course, where some specific aspects of the general relativistic dynamics will be discussed, compared to the analogous mechanisms in Newtonian gravity, when allowed. The main arguments included in the course are: -Einstein equations and their comparison with Newtonian gravity: time dependence, non harmonicity tensorial character, non-linearity. -Gravitational waves: generation and detection; weak and strong gravitational waves, effective one body formalism. -Dragging effects and weak and strong gravitomagnetism, with applications to the motion of massive bodies and galaxies However, modifications on the program can be considered on demand, to adapt the details of the lessons to the specific needs of the students.

Complements of theoretical physics (Sergio Cacciatori, I anno) 
This is a 20-hour course, with the aim of presenting some advanced topics in theoretical physics, related with the physics of the standard model and/or general aspects of theoretical physics. The main arguments proposed by the course are: -Symmetries in quantum field theory: Lie groups, spontaneous symmetry breaking of global symmetries and local symmetries, symmetries in path integral formalism, anomalies. -Feynman integrals in classical and quantum theories. Methods of computation of the Feynman integrals and related twisted cohomology. -The geometry of the Standard Model of Particles and possible extensions to grand unification models. According to the interests of the participating students, it is possible to consider a short introduction to all such arguments, or to develop more deeply one of them if needed.
 

Theory of Cosmological Perturbations (Oliver Piattella, I anno) 
Perturbations about the FLRW metric and the problem of the gauge; the scalar-vector-tensor decomposition; Einstein equations and Boltzmann equations for perturbations; primordial modes: adiabaticity and isocurvature initial conditions; the inflationary paradigm; solutions for the evolution of perturbations; the matter power spectrum and the CMB power spectra.
 

Basics and applications of FPGAs (Alessia Allevi, Andrea Abba, Stefano Carsi, Marco Lamperti, I anno) 
The use of FPGA systems is motivated by their ability to provide fast, deterministic, and real-time processing of signals. The course begins with an introduction to FPGA systems, explaining what they are, what they are used for, the available alternatives, and how they are programmed (2 hours). It then focuses on the use of Sci-Compiler, a dedicated software, to program a digital charge integration system, including hands-on sessions using personal computers and an evaluation board provided by the instructors (14 hours). Finally, a laboratory use case is presented involving a 14-bit digitizer for acquiring signals from a pair of silicon photomultipliers used in the characterization of quantum light (4 hours).
 

Numerical methods for astrophysics (Alessandro Lupi, I anno) 
The course "Numerical methods for astrophysics" is meant to introduce state-of-the-art numerical modelling techniques employed in astrophysics and will cover 20 hours. In detail, the following topics will be covered: - Newtonian dynamics and the N-body problem (grid-based vs particle-based methods) - Advanced techniques for computational hydrodynamics: adaptive mesh refinement vs moving mesh vs mesh-free methods, advantages and limitations - High performance computing: code development and optimization.
 

Time series analysis for astrophysicists (Stefano Covino, I e II anno) 
Time series are ubiquitous in astrophysics. This course is aimed at providing PhD students the main capabilities to extract physical information with state-of-the-art statistical inferences from the available datasets. We will refer to real science cases developed in the astrophysical literature, yet the discussed methodologies could be of definite interest to anyone involved in quantitative analysis of data in a temporal (or spatial) sequence in any field of modern physics, economy, engineering and social sciences. At the end of the course students will be able to: 
•carry out analysis of any statistical problem in a full Bayesian framework
 • properly model time series to derive meaningful statistical inferences about stationarity,
 • short and long-term memory behavior;
 • deal with data irregular spaced and/or affected by correlated noise • 
apply big-data techniques to carry out the analyses of typical large datasets obtained by modern astrophysical facilities. 
More specifically the main topics of the course are: 
• Time (and spatial) variability in astrophysics 
• Time- domain analysis and auto-regressive processes 
• Irregular sampling, Lomb Scargle periodograms 
• Case studies: ANG variability 
• Advanced topics: non-parametric analysis • Matching filter • Case study: LIGO/Virgo gravitational wave signals • Big-data machine learning and intelligent systems for time- series analysis • Case studies: spatial variability /CMB, large scale structure)
 

QFT on curved spacetimes (Ugo Moschella, I e II anno) 
The course is intended as a short introduction to Quantum Field Theory on curved spacetimes. In doing this I will also discuss some topics in General Quantum Field Theory that are not always taught in standard QFT courses. 
Topics that will be covered are: 1) Quantization. CCR and CAR algebras. Representations of the commutation rules. The Stone-Von Neumann theorem and its failure. 
2) Quantization of fields. Canonical quantization of the Klein Gordon field in Minkowski spacetime. Commutators. Propagators. Two-point functions. Quantum fields as distributions. N point functions. Reconstruction theorem. 
3)The spectral condition and its consequences. 
4)KMS equilibrium states. Bogoliubov transformations. Generalized Bogoliubov transformations. The Unruh effect 
5) Canonical Quantization of fields in curved spacetimes. General formalism. The Local Hadamard condition. The microlocal spectrum condition. Renormalization. The Casimir effect. 
6) Examples. Expanding universes. Bogoliubov transformations. Particle creation by expansion. 7)
Thermal equilibrium states. The Hawking effect. 
8)Quantum field theory on the de Sitter spacetime. De Sitter invariant vacua. Preferred vacuum. The thermal interpretation. Massless Fields. Applications. Instabilities. 
9) Quantum field theory on the anti de Sitter spacetime. The AdS-CFT correspondence.
Textbooks N.D. Birrell, P. C. W. Davies. Quantum Fields Curved Space. Cambridge University Press (1982) S. A. Fulling. Aspects of quantum field theory in curved space-time. Cambridge University Press (1989) R.M. Wald. Quantum field theory in curved space-time and black hole thermodynamics. Chicago U. (1995)
 

Astrochemistry (Alessandro Lupi, I anno)
 - Introduction to Astrochemistry. 
- The interstellar medium: physical conditions, regions and different components. 
- Radiative and collisional excitation processes. 
- Basic processes in Astrochemistry. 
- Gas-phase processes. 
- Photochemistry: ionisation and dissociation. 
- Cosmic rays. 
- Solids in the interstellar medium. 
- Thermal processes. 
- Case study: Chemistry in molecular clouds (the molecular factory)
 

Probing Vibrational Modes with Light: Principles and Practice of Raman Spectroscopy (Marco Lamperti, I e II anno) 
This laboratory course provides a self-contained introduction to Raman spectroscopy, combining theoretical foundations with hands-on laboratory sessions. The course follows a research-driven approach: after a theoretical introduction and a laboratory session covering instrument usage and data analysis on predefined samples, the students will work on designing and carrying over a final experiment. The exam will consist in live discussion of the results during the final project. 
Program summary: Theoretical foundations (3 lessons, 2h each) 
-Physical principles of Raman scattering: classical and quantum description of light-matter interaction, vibrational selection rules, spectral interpretation 
-Instrumentation of a dispersive Raman spectrometer: light sources, optical components, detector physics, noise sources and signal-to-noise optimization

Laboratory sessions (2 lessons, 4h each) 
-Overview of the setup, instrument operation, spectral acquisition and processing 
-Molecular vibrations in pharmaceutical solids (e.g. paracetamol, caffeine): spectral assignment and polymorphism 
-Phonons in inorganic materials (TiO₂, graphene if available): phase identification and layer characterization 
-Overview of advanced techniques (FT-Raman, UV resonance Raman, Raman imaging) as a perspective module, expandable depending on student's interests

Final project (3 lessons, 2+3+3h)
 -Discussion of proposals with the teacher and design of the experiment 
-Investigation of the research question using Raman spectroscopy and possibly other techniques (such as infrared and UV-VIS spectroscopy)
 -Depending on the outcomes, there is the possibility of extending the collaboration beyond the course with the goal of contributing to an original research publication

Laser-Driven Radiation Sources: Science, Technology and Applications (Matteo Clerici, I e II anno) 
This short course introduces students to the technological aspects and applications of laser driven sources of radiation, one of the most active areas of research in laser physics today. The course begins with a brief introduction to ultrafast lasers, followed by an overview of the science, technology, impact, and applications of state-of-the-art secondary sources. These include parametric amplifiers (mid-infrared sources), optical rectification or photoconductive switching (THz sources), and non-perturbative light-matter interactions (high-order harmonic generation).

Fundamentals and Applications of Optical Metrology (Lucia Caspani, I e II anno) 
This short course introduces students to the basic concepts of optical metrology and provides an overview of the current state-of-the-art for some of its most advanced and widespread applications. The course begins with an introduction to the theoretical aspects of optical metrology and the physical mechanisms underpinning its applications. It then analyzes examples of transformative metrological applications, such as interferometry (empowering the observation of phenomena like gravitational waves), spectroscopy (e.g., time-resolved spectroscopy with unparalleled sensitivity), and dual-comb spectroscopy (used e.g., astrophysical observations).
 

Advanced Concepts of Light-matter interaction and their applications (Ottavia Jedrkiewicz, I e II anno) 
This short course introduces students to the basic concepts of light-matter interactions and their applications. It begins with an introduction to laser physics and the different regimes of light matter interaction driven by intense laser fields. The course then focuses on key applications of lasers, such as micromachining (cutting, drilling, and machining of transparent materials), medical applications (e.g., eye surgery), and applications to astrophysics (spectroscopy and interferometry).

Selected topics in astrophysical fluid dynamics (Mattia Sormani, I e II anno) 
Argomenti trattati (un sottoinsieme di) - Fundamentals of hydrodynamics: continuity and Euler equations, equation of state, conservation of mass/momentum/energy, viscosity and thermal conduction, Lagrangian vs Eulerian views, vorticity equation, Kelvin circulation theorem, rotating frames, radiative heating & cooling, Reynolds number
 - Fundamentals of magneto-hydrodynamics: MHD equations, induction equation, magnetic pressure and tension, magnetic flux freezing, magnetic fields amplification. - Hydrostatic equilibrium: polytropic and isothermal spheres, polytropic and isothermal slabs, application. Chandrasekhar upper mass limit for white dwarfs -
 Spherical steady flows: Parker solar wind and Bondi spherical accretion
 - Waves: sound waves, water waves, group velocity, analogy between shallow water theory and gas dynamics, MHD waves (Alfvén waves, fast and slow waves), internal gravity waves
 - Shocks: steepening of sound waves and the formation of shocks, 1D jump conditions at discontinuity (Rankine-Hugoniot conditions), Mach number, MHD shocks, shock thickness in the presence of viscosity 
- Spherical blast waves: strong explosion in uniform atmosphere, Sedov-Taylor self-similar solution, application: supernovae 
- Instabilities: Kelvin-Helmholtz instability, Thermal instability, Rayleigh instability, rotational instability and Rayleigh criterion, magneto-rotational instability, Jeans instability
 - Gravity: Legendre expansion, Gauss’s Law, Poisson equation, Tidal forces, Virial theorem. Applications: calculation of moon tides, stability of satellites in orbit around the Earth 
- Elements of turbulence, Kolmogorov’s theory 
- Rotating equilibria and thick discs: barotropic equilibria and Taylor-Proudman theorem, baroclinic equilibria, Solberg-Hoiland stability criterion 
- Accretion discs: inviscid thin disc, viscous evolution of a thin disc and spreading of a thin ring, steady-state viscous thin discs, angular momentum transport, Shakura-Sunyaev alpha-disc “standard” model, emitted spectrum, the Eddington limit, angular momentum transport in discs
 - Effects of rotation on waves, epicyclic frequency and Lindblad resonances, density waves in discs, Toomre instability, Papaloizou-Pringle instability
 

Scientific Communication and Investigative Journalism: Methods, Risks and Case Studies
Scientific knowledge does not circulate in a vacuum: it is constantly mediated, interpreted, and sometimes distorted by communication processes, especially in contexts of uncertainty, crisis, or high public impact. This course aims to provide PhD students in physics with the conceptual and practical tools needed to understand how scientific information is produced, communicated, and received outside the academic environment. The first part of the course introduces the fundamentals of scientific communication, focusing on the differences between technical, institutional, and media narratives. Particular attention is given to the structure of information, the role of simplification, and the risks of misinterpretation when complex physical concepts are translated into public discourse. The second part explores the dynamics of crisis communication through historical and contemporary case studies, such as Chernobyl and Fukushima, highlighting the interplay between scientific facts, political decisions, and media representation. Students will analyze how different truths, technical, official, and historical can diverge, and what implications this has for public understanding. The final part is dedicated to investigative approaches in science journalism. It provides methods to critically read scientific sources, interpret data and publications, identify biases, and distinguish between reliable information and misinformation. Practical exercises and discussion sessions will allow students to apply these tools to real-world scenarios. By the end of the course, participants will have developed a clearer awareness of the communication dimension of science, and will be better equipped to engage responsibly with the public, institutions, and the media.