Course name  Note  Period  Time Table 


ALGEBRAIC GEOMETRY I (GE410)The course might be held in Italian  Semester I  
 
semester I  
 
COMMUTATIVE ALGEBRA (AL410)The course might be held in Italian  Semester I  
 
CRYPTOGRAPHY WITH PUBLIC KEY (CR410)The course might be held in Italian  Semester I  
 
semester I  
 
Semester I  
 
Semester I  
 
Semester I  
 
Semester I  
 
Semester II  
 
Semester II  
 
COMPUTATIONAL FINANCE (MF410)The course might be held in Italian  Semester II  
 
GRAPH THEORY (GE460)The course might be held in Italian  Semester II  
 
semester II  
 
semester II  
 
MATHEMATICAL PHYSICS (FM410)The course might be held in Italian  Semester II  
 
Semester II  
 
Semester II  
 
Semester II  
⇧  
RIEMANNIAN GEOMETRY (GE430)  semester II  
 
Semester II  
 
THEOREMS IN LOGIC (LM420)The course might be held in Italian  Semester II  
 
THEORIES IN LOGIC (LM430)The course might be held in Italian  Semester II  
 
FUNCTIONAL ANALYSIS (AM450)36 h  Semester II   

Course name  Note  Period  Time Table 


semester I  
 
Semester I  
 
Semester I  
 
semester I  
⇧  
ALGEBRAIC GEOMETRY II (GE510)The course might be held in Italian  Semester II  
 
Semester II  
 
semester II  
 
semester II  
 
semester II  
 
Semester II  
 
semester II  

Course name  Note  Period  Time Table 


PROJECTIVE SPACES AND BIRATIONAL TRANSFORMATIONS (GE520)
Projective spaces and birational transformations (GE520)PROGRAM  PROJECTIVE SPACES AND BIRATIONAL TRANSFORMATIONS (GE520)GOALS  
 
KINTIC THEORY OF GASES AND THE KAC MODEL  KINTIC THEORY OF GASES AND THE KAC MODELAbstract: The aim of the course is to present basic problems of kinetic theory and statistical mechanics using Kac's model as a starting point for physical ideas and rigorous results. In the first part of the course I will give a presentation of the basic ideas of Statistical Mechanics and the heuristic derivation of the Boltzmann equation. I will then introduce Kac's model and present classic results such as: relaxation towards equilibrium, propagation of chaos and the derivation and solutions of the BoltzmannKac equation. After that I will discuss the evolution of Kac's model when in contact with a thermostat or with a thermal bath. Finally I will discuss more recent results depending on the time left and the interests of the students.  April May 2022 
 
 
RATIONAL SIMPLE CONNECTEDNESS IN COMPLEX ALGEBRAIC GEOMETRY
Rational simple connectedness in complex algebraic geometryThe main goal of this course will be to study a very recent notion in complex algebraic geometry, which generalises rational connectedness: the rational simple connectedness. This notion has, at least conjecturally, striking applications to the existence of rational sections for rationally connected fibrations over surfaces. It is well known that rationally connected fibrations over curves have sections, but the problem becomes much more subtle over higher dimensional base: it is very easy to construct conic bundles over surfaces having no rational sections. Just recently de Jong and Starr introduced the notion of rational simple connectedness for polarised varieties, while looking for sufficient In this course I will discuss the following topics: 1. rational curves on Fano varieties;
2. rational simple connectedness of complete intersections;
3. rational simple connectedness of rational homogeneous varieties and Serre's conjecture II;
4. rational simple connectedness and higher Fano varieties.
 JuneJuly 2022 
 
 
STACKS AND MODULI
STACKS AND MODULIThe course will give an introduction to the theory of algebraic stacks,  March  May , 2022 
 
 
HANDS ON CONTINUUM MECHANICS
(MINI COURSE)
Hands on Continuum Mechanics (mini course)Goal: understand the fundamentals of continuum mechanics through worked examples. Participants will tackle some typical problems of continuum mechanics, and will learn to implement a problem using the weak formulation into the COMSOL software and to discuss the solution.  March 2022 
 
 
INTRODUCTION TO EXPANSIONS IN NONINTEGER BASES
Introduction to expansions in noninteger bases
expansions. This led to hundreds of papers in the past thirty years. We propose an introduction to this subject, which is still rich in open problems. The plan of our course is the following:

References: • A. R´enyi, Representations for real numbers and their ergodic properties, Acta Math. Hungar. 8 (1957) 477–493. • P. Erd?os, I. Jo´o, P V. Komornik, Characterization of the unique expansions 1 = 1i =1 q−ni and related problems, Bull. Soc. Math. France 118 (3) (1990) 377– 390. • V. Komornik, P. Loreti, Unique developments in noninteger bases, Amer. Math. Monthly 105 (7) (1998) 636–639. • M. de Vries, V. Komornik, Unique expansions of real numbers, Adv. Math. 221 (2) (2009) 390–427. • V. Komornik, A. C. Lai, M. Pedicini, Generalized golden ratios of ternary alphabets, J. Eur. Math. Soc. (JEMS), 13 (4) (2011) 1113–1146. • V. Komornik, D. Kong, W. Li, Hausdor↵ dimension of univoque sets and devil’s staircase, Adv. Math. 305 (2017) 165–196.  May 2022 
 
⇧  
APPLICATIONS OF FOURIER ANALYSIS IN THE THEORY AND CONTROL OF PDES
Applications of Fourier analysis in the theory and control of PDEsFourier analysis is historically strongly linked to the resolution of PDEs with the fundamental example of the heat equation that was initially introduced by Fourier himself. In this course, we will first give an introduction of the different concepts entering in the Fourier analysis.  October 2021 
 
 
PROGRAMMING IN PYTHON AND MATLAB (IN400)  semester I 
 
 
AN INTRODUCTION TO CHEEGER'S ENERGY AND ANALYSIS IN METRIC MEASURE SPACES
An introduction to Cheeger\'s energy and Analysis in metric measure spacesMany interesting objects, like the Dirichlet energy or the heat equation However, recently the Dirichlet energy has been generalized to Cheeger's energy, which requires only functions defined on a metric space and a Borel measure to calculate the integrals. In this course, we try to give an introduction to Cheeger's energy: we shall give two different definition of Cheeger's energy and prove that they are equivalent. For the proof, we need to introduce the basic definitions and theorems of optimal transport, Wasserstein distance and gradient flows in metric spaces. If there is time, we are going to show a version of the theorem of Otto, Kinderlehrer and Jordan, which says that the heat equation is the gradient flow of the entropy functional in the metric space of measures with the 2Wasserstein distance.  Starting January 2022 
 
 
GEOMETRY OF PROJECTIVE ALGEBRAIC VARIETIES
EXAMPLES, PROBLEMS, EXERCISES
Geometry of projective algebraic varieties Examples, problems, exercisesAbstract:  Starting March 22, 2022 
 
 
TOWARDS INFORMATION THEORY, NEURAL NETWORKS, AND BEYOND
(READING COURSE)
Towards Information theory, neural networks, and beyond (Reading course)Topics:  Starting November 12, 2021 
 

Institution  

Via della Vasca Navale 84
00146 Roma  Italia
tel: +39 06 57330007
fax: +39 06 57337102
Via della Vasca Navale 84
L.San Leonardo Murialdo 1
00146 Roma  Italia
Direttore : Prof. Roberto Raimondi
direttore_matfis@fis.uniroma3.it
Responsabile Area Amministrativa: Rossella Mantini
amm.matematicafisica@uniroma3.it
Responsabile Area Ricerca: Virgilio Lo Presti
ricerca.matematicafisica@uniroma3.it
Responsabile Area Didattica: Valentina Feliciello
didattica.matematicafisica@uniroma3.it
Copyright© 2014 Dipartimento di Matematica e Fisica