Insegnamenti erogati dal corso di dottorato in Fisica
Computational Methods for Tomographic Image Reconstruction in Medical Imaging
Area: Applied Physics
- Teacher: N. Belcari, D. Panetta
- Programmed Period: mid February – mid May
- Structure: 40 hours total
- Language: English
The course provides an introduction to the problem of image reconstruction from projections, with particular emphasis on Computed Tomography (CT) and Positron Emission Tomography (PET). Even though this topic is often seen as a branch of pure mathematics, referred to as Tomographic Reconstruction, it is indeed a strongly multidisciplinary domain involving, physics, engineering, computer science and, of course, any discipline relevant for the final application (not just medical) for which the above-mentioned imaging modalities are used.
After an introduction to CT and PET imaging principles and related technologies the student will be guided through the mathematical formalization of the image reconstruction process and several computational techniques are introduced and discussed. About 50% of the hours will be dedicated to practical exercises on image reconstruction. A background of scientific programming in Python/Numpy is necessary to get a fruitful understanding of the sample code, listings and Jupyter notebooks provided during the course, even though this is not required for the comprehension of the theory itself.
Lectures will be held in class twice a week.
At the end of the course, students are expected to individually complete a project in which they provide a practical solution to an image reconstruction problem, starting from simulated and/or experimental projection data.
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The Hubble Tension: Measuring Cosmic Expansion in the Modern Era
- Area: Astronomy and Astrophysics
- Teachers: M. Cignoni, M. Bischetti, S. Degl’Innocenti, A. Pallottini, P.G. Prada Moroni, A. Ricciardone
- Programmed Period: second semester
- Structure: 40 hours
- Language: English
Since the seminal work regarding the expansion of the Universe from Hubble in 1929, the determination of the Hubble constant, H0, has been central in guiding our predictions for the cosmic structure formation and galaxy evolution.
In this context, the “Hubble tension” refers to the discrepancy of about 6 km/s/Mpc (about 4 ) between the result obtained in the late Universe (redshift z<2, e.g., from the distance ladder method) and in the early Universe (redshift z~1100, e.g., from the Cosmic Microwave Background (CMB) method), that seems to be lingering in the data since about 2015. If the measurements performed using different methods are correct, this represents a statistically relevant tension and a possible hint of new physics.
A promising avenue to unravel this puzzle is provided by the observation of gravitational waves from coalescing compact binaries. Such signals provide, in fact, a distance-ladder-free determination of the luminosity distance to a source, thus circumventing potential systematic biases implicit in the Supernovae measurements. However, the redshift is, with a few notable exceptions, not measurable from gravitational waves alone. Several methods have been proposed, each with its strengths and weaknesses, and a gravitational wave determination of H0 is now possible.
In this course, we will address the Hubble tension topic by discussing both early and late universe determinations (i.e., Supernovae, CMB and GWs), possible solutions, and implications for astrophysics and cosmology.
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Non-perturbative Aspects of Quantum Field Theories
Area: Theoretical Physics
- Teachers: V. Alba, S. Bolognesi, M. Burrello, M. D’Elia, A. Vichi
- Programmed period: December – February
- Structure: 4 modules of 20 hours each
- Language: English
The purpose of the course is to provide a thorough knowledge about the main approaches used in theoretical physics to study strongly coupled system, which cannot be investigated by standard perturbative tools. Within the standard model of particle physics, this happens for Quantum Chromodynamics (QCD) at the low energy hadronic scale. Analogous non-perturbative approaches are required in condensed matter and in the theory of critical phenomena, where one usually deals with strongly coupled systems. The course is divided into four parts, each of them corresponding to 3 CFU, which are related to each other by a common language and tools and by various common aspects, but are anyway self-consistent by themselves. The first part (M. D’Elia) deals with the Lattice formulation of Quantum Gauge Theories; the second part (S. Bolognesi) is dedicated to the investigation of the role of Topological Solitons in QFT; the third part (V. Alba and A. Vichi) focusses on the investigation of Conformal Symmetry and Conformal Field Theories; the last part is dedicated to the study of two-dimensional quantum models with topological order and the Hamiltonian formulation of lattice gauge theories with discrete groups. The student can make a selection among these parts. The expected competences to be acquired by the student, to be verified in the final oral exam, consist both in specific knowledges about the various topics and in the ability to connect and interrelate different concepts.
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Current Trends in Quantum Matter
- Area: Condensed Matter Physics
- Teachers: M.L. Chiofalo, A. Tredicucci
- Programmed Period: February – May 2027
- Structure: 18 hours
- Language: English
The course comprises the discussion of a series of seminars (9, 2 hours each), regarding the most cutting-edge quantum matter physics of the moment. Topics will include:
- Strongly correlated many-body systems, in particular electrons and ultracold atoms
- Fluids of light
- Cavity modified interactions
- Systems in reduced dimensionality
- Driven-dissipative open quantum systems
- Quantum metrology
- Analog quantum systems
The seminars will be delivered by theorists and experimentalists leading these fields of research. Overviews will be provided on concepts and tools, and on pertinent models of interacting quantum matter, with an interdisciplinary approach.
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Statistical Analysis Laboratory
- Area: Experimental Particle Physics
- Teacher: Giovanni Punzi
- Programmed Period: Feb-May 2027
- Structure: 40 hours total
- Language: English
The course will be based on a set of guided exercises in computational statistics of gradually increasing complexity, progressing from basic simulations, estimators, confidence intervals, fits, up to realistic case studies.
Lectures will be held in class once or twice a week. In addition to discussion of general methodologies, students will be given specific directions about the problems and will then work on them individually. Each student can perform their work using their own preferred software platform. It is a precondition of this course that students have access, and the needed knowledge to use a programmable software system capable of performing simple calculations, random number generation, histogramming and plotting. Students are expected to turn in the results at the next class, where they will be discussed, and will eventually produce written summaries. The concluding case studies will exemplify in a reduced form some specific real research problems. More time will be allowed for their solution, and the corresponding written reports will be part of the final exams.
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Detailed program
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