Ph.D. in Mathematics

Courses a.y. 2020-2021

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BASIC ▾ N : 26 ⇧

Course name	Note	Period
ALGEBRAIC GEOMETRY I (GE410)	ALGEBRAIC GEOMETRY I (GE410) The course might be held in Italian	Semester I
Angelo Lopez ( lopez@mat.uniroma3.it - Dipartimento di Matematica e Fisica ) ⇧
COMMUTATIVE ALGEBRA (AL410)	COMMUTATIVE ALGEBRA (AL410) The course might be held in Italian	Semester I
Margherita LELLI CHIESA ( margherita.lellichiesa@uniroma3.it - Universita degli Studi Roma TRE ) ⇧
COMPUTABILITY AND COMPLEXITY (IN410)		Semester I
Marco PEDICINI ( marco.pedicini@uniroma3.it - Dipartimento di Matematica e Fisica ) ⇧
CRYPTOGRAPHY WITH PUBLIC KEY (CR410)	CRYPTOGRAPHY WITH PUBLIC KEY (CR410) The course might be held in Italian	Semester I
Francesca MEROLA ( merola@mat.uniroma3.it - Dipartimento di Matematica e Fisica ) ⇧
EDUCATIONAL & OUTREACH -COMUNICAZIONE DELLA SCIENZA (FS490)		semester I
( - To be defined ) ⇧
ORDINARY DIFFERENTIAL EQUATIONS (AM430)		Semester I
Luigi CHIERCHIA ( luigi@mat.uniroma3.it - Dipartimento di Matematica e Fisica ) ⇧
PARALLEL AND DISTRIBUTED COMPUTING (IN480)		Semester I
Alberto PAOLUZZI ( paoluzzi@dia.uniroma3.it - Dipartimento di Matematica e Fisica ) ⇧
PROBABILITY THEORY (CP410)		Semester I
Elisabetta CANDELLERO ( ecandellero@mat.uniroma3.it - Dipartimento di Matematica e Fisica ) ⇧
PROGRAMMING LANGUAGES (IN490)		Semester I
Flavio LOMBARDI ( lombardi@mat.uniroma3.it - CNR ) ⇧
QUANTUM MECHANICS (FS420)		Semester I
( - to be defined ) ⇧
ALGEBRAIC TOPOLOGY (GE450)		Semester II
Andrea BRUNO ( bruno@mat.uniroma3.it - Dipartimento di Matematica e Fisica ) ⇧
ALGORITHMS IN CRYPTOGRAPHY (IN450)		Semester II
Marco PEDICINI ( marco.pedicini@uniroma3.it - Dipartimento di Matematica e Fisica ) ⇧
APPLIED AND INDUSTRIAL MATHEMATICS (MA410)	APPLIED AND INDUSTRIAL MATHEMATICS (MA410) The course might be held in Italian	Semester II
Roberto FERRETTI ( ferretti@mat.uniroma3.it - Dipartimento di Matematica e Fisica ) ⇧
COMBINATORIAL OPTIMIZATION (IN440)		Semester II
Marco LIVERANI - liverani@mat.uniroma3.it ⇧
COMPUTATIONAL FINANCE (MF410)	COMPUTATIONAL FINANCE (MF410) The course might be held in Italian	Semester II
Francesco Cesarone ( francesco.cesarone@uniroma3.it - Universita degli Studi Roma TRE ) ⇧
GRAPH THEORY (GE460)	GRAPH THEORY (GE460) The course might be held in Italian	Semester II
ANA Margarida MASCARENHAS MELO ( melo@mat.uniroma3.it - Dipartimento di Matematica e Fisica ) ⇧
INTRODUZIONE ALLA LOGICA (LM400)		semester II
Vito Michele ABRUSCI ( michele.abrusci@tlc.uniroma3.it, vitomichele.abrusci@uniroma3.it - Universita degli Studi Roma TRE ) ⇧
MATHEMATICAL PHYSICS (FM410)	MATHEMATICAL PHYSICS (FM410) The course might be held in Italian	Semester II
Guido GENTILE ( gentile@mat.uniroma3.it - Dipartimento di Matematica e Fisica ) ⇧
MATHEMATICS TEACHING LABORATORY (MC430)		Semester II
Corrado FALCOLINI ( falco@mat.uniroma3.it - Universita degli Studi Roma TRE ) ⇧
NUMERICAL ANALYSIS (AN420)		Semester II
SIMONE CACACE ( cacace@mat.uniroma3.it - Dipartimento di Matematica e Fisica ) ⇧
PHYSICS TEACHING LABORATORY (FS410)		Semester II
Roberto Di Nardo ( roberto.dinardo@uniroma3.it - Dipartimento di Matematica e Fisica ) Domizia ORESTANO ( orestano@fis.uniroma3.it - Dipartimento di Matematica e Fisica ) ⇧
SOBOLEV SPACES AND PDE (AM420)		Semester II
Emanuele HAUS ( ehaus@mat.uniroma3.it - Dipartimento di Matematica e Fisica ) ⇧
STOCHASTIC PROCESSES (CP420)		Semester II
Fabio MARTINELLI ( martin@mat.uniroma3.it - Dipartimento di Matematica e Fisica ) ⇧
THEOREMS IN LOGIC (LM420)	THEOREMS IN LOGIC (LM420) The course might be held in Italian	Semester II
Lorenzo TORTORA DE FALCO ( lorenzo.tortoradefalco@uniroma3.it - Dipartimento di Matematica e Fisica ) ⇧
THEORIES IN LOGIC (LM430)	THEORIES IN LOGIC (LM430) The course might be held in Italian	Semester II
Lorenzo TORTORA DE FALCO ( lorenzo.tortoradefalco@uniroma3.it - Dipartimento di Matematica e Fisica ) ⇧
FUNCTIONAL ANALYSIS (AM450)	FUNCTIONAL ANALYSIS (AM450) 36 h	Semester II -
Luca BATTAGLIA ( lbattaglia@mat.uniroma3.it - Dipartimento di Matematica e Fisica ) ⇧

INTERMEDIATE ▾ N : 13 ⇧

Course name	Note	Period
DISCRETE PROBABILITY (CP450)		semester I
Alexandre STAUFFER ( astauffer@mat.uniroma3.it - Dipartimento di Matematica e Fisica ) ⇧
MACHINE LEARNING (IN550)		Semester I
Vincenzo BONIFACI ( vincenzo.bonifaci@uniroma3.it - Dipartimento di Matematica e Fisica ) ⇧
NUMERICAL ANALYSIS FOR PDES (AN430)		Semester I
Luciano TERESI ( luciano.teresi@uniroma3.it - Dipartimento di Matematica e Fisica ) ⇧
REURAL NETWORKS (FS480)		semester I
( paolo.delgiudice@roma1.infn.it - Universita La Sapienza ) ⇧
ALGEBRAIC GEOMETRY II (GE510)	ALGEBRAIC GEOMETRY II (GE510) The course might be held in Italian	Semester II
Angelo Felice LOPEZ ( lopez@mat.uniroma3.it - Dipartimento di Matematica e Fisica ) ⇧
ELLIPTIC CRYPTOSYSTEMS (CR510)		Semester II
Francesco PAPPALARDI - ⇧
IRRATIONALITY, TRANSCENDENCE AND DIOPHANTINE EQUATIONS (TN520) - Irrationality, transcendence and diophantine equations (TN520) - Introduction to algebraic number theory: Rings of integers in number fields and unique factorisation of ideals. Absolute values in number fields. The Weil Height and the Mahler measure: Definitions and properties. The product Formula Northcott’s Theorem. Kroneker’s Theorem. Thue equations: Thue’s Theorem on diophantine approximation. Siegel’s Lemma. Thue equations have a finite number of integer solutions. Arithmetic dynamics: (Pre)periodic points. The canonical height. Rational functions. Diophantine equations in roots of unity: Revision about roots of unity and cyclotomic polynomials. The Theorem of Ihare-Serre-Tate. Equidistribution: Definitions and examples. Bilu’s Theorem. Bogomolov’s Conjecture.		Semester II
Fabrizio BARROERO ( barroero@mat.uniroma3.it - Dipartimento di Matematica e Fisica ) ⇧
LINEAR ALGEBRA FOR MACHINE LEARNING (GE530)		semester II
⇧
LOCIG THEORY 1 (LM510)		semester II
Roberto MAIELI ( maieli@uniroma3.it - Dipartimento di Matematica e Fisica ) ⇧
MATHEMATICAL PHYSICS APPLICATIONS (FM510)		semester II
Elisabetta SCOPPOLA ( scoppola@mat.uniroma3.it - Dipartimento di Matematica e Fisica ) Luciano TERESI ( luciano.teresi@uniroma3.it - Dipartimento di Matematica e Fisica ) ⇧
MONTECARLO METHOD (FS510)		Semester II
Roberto FRANCESCHINI ( franceschini@fis.uniroma3.it - Dipartimento di Matematica e Fisica ) ⇧
PRINCIPLES OF ASTROPHYSICS (FS470)		semester II
Fabio LA FRANCA ( lafranca@fis.uniroma3.it - Dipartimento di Matematica e Fisica ) Giorgio MATT ( matt@fis.uniroma3.it - Dipartimento di Matematica e Fisica ) ⇧
RIEMANN SURFACES (GE470)		semester II
Alessandro VERRA ( verra@mat.uniroma3.it - Dipartimento di Matematica e Fisica ) ⇧

SPECIAL ▾ N : 4 ⇧

Course name	Note	Period
PROJECTIVE SPACES AND BIRATIONAL TRANSFORMATIONS (GE520) (to be defined) Projective spaces and birational transformations (GE520) PROGRAM 1) Linear systems of hypersurfaces in Pn Generalities and basic notions, examples in plane and space geometry. 2) Corrispondences in Pn x Pn Intersection theory, Segre classes, numerical characters of a correspondence. Examples. 2) Cremina transformations Linear system of rational hypersurfaces. Homaloidal linear systems Basic Cremona transformations of Pn. 4) In P2 Quadratic transformations, birational involutions, de Jonquiéres trasformations. Structure of the group. Some finite subgroups. 5) In P3: Linear system of rational surfaces. Transformations defined by quadrics or cubicss. Their inverse transformations. 6) Factorization in P3 Birational maps of P3 and Mori theory. Classification of elementary links with applications. Noether-Fano inequalities. I teoremi di Max Noether per P2 e di Hilda Hudson per P3. Cenni storici e risultati recenti sul gruppo di Cremona. - I. Dolgachev ‘Classical Algebraic Geometry’, Cambridge University Press 2012 - I. Dolgachev ‘Lectures on Cremona Transformations, Ann Arbor-Rome’ 2010 -11 http://www.math.lsa.umich.edu/~idolga/cremonalect.pdf - I. Cheltsov, C. Shramov, ‘Cremona Groups and the Icosahedron’ CRC Press New York 2016 - I. Cheltsov, C. Shramov, Three embeddings of the Klein simple group into the Cremona group of rank three, Transformation Groups - A. Verra ‘Lectures on Cremona Transformations’, School and Workshop, Torino 2006, pdf. - Si vedano inoltre le voci ‘Cremona group’ e ‘Cremona transformation’ in Encyclopedia of Mathematics. European Math. Society Press	PROJECTIVE SPACES AND BIRATIONAL TRANSFORMATIONS (GE520) GOALS Birational transformations play a central role in algebraic geometry, since a main goal of this discipline is the birational classification of varieties defined by polynomial equations. The course aims to introduce, by elementary tools and examples, the birational transfomations of a complex projective space in itself. These transformations forma group which is well known as the Cremona group. This group has a remarkable interest in geometry and more generally in mathematics, for instance in algebra and in complex dynamics. The structure of it, relatively well known up to dimension two, is far from being completely understood in higher dimension. The study of Cremona transformations will bring the students to meet, concretely in the case Pn, modern and classical methods and techniques from birational geometry. Some relevant examples, showing the importance of the Cremona group for studying algebraic varieties will be also introduced.
Alessandro VERRA ( verra@mat.uniroma3.it - Dipartimento di Matematica e Fisica ) ⇧
CURVES AND BUNDLES ON CURVES WITH TRIVIAL CANONICAL BUNDLE Curves and bundles on curves with trivial canonical bundle Starting from March 2021, two 2 hours lectures per week PROGRAM Review of Brill-Noether Theory. Brill-Noether theory for curves on a K3 surface. The Lazarsfeld-Mukai bundle. Lazarsfeld proof of Brill-Noether-Petri Theorem. Constancy of Clifford index for curves on a K3 surface: Donagi-Morrison Conjecture. Clifford dimension and exceptional curves: Eisenbud-Lange-Martens-Schreyer Conjecture. Mukai’s Program: non-abelian Brill-Noether Theory of curves on a K3 surface. Reconstruction of a K3 surface from its hyperplane section. The Wahl map and Wahl Conjectures: characterization of Brill-Noether-Petri general curves on a K3 surface. Brill-Noether Theory of curves on an abelian surface. The second Gauss-Wahl map and hyperplane sections of abelian surfaces. Severi Varieties on K3 and abelian surfaces. PREREQUISITES: basic knowledge of algebraic geometry (schemes and sheaf cohomology); curves (Arbarello-Cornalba-Griffiths-Harris, volume 1)		March, 2021
Andrea BRUNO ( bruno@mat.uniroma3.it - Dipartimento di Matematica e Fisica ) Margherita LELLI CHIESA ( margherita.lellichiesa@uniroma3.it - Dipartimento di Matematica e Fisica ) ⇧
INTRODUCTION TO KAC'S MODEL AND ITS RELATIONS WITH STATISTICAL MECHANICS Introduction to Kac\'s model and its relations with Statistical Mechanics The aim of the course is to present basic problems of kinetic theory and statistical mechanics using Kac's model as a starting point and testing ground for physical ideas and rigorous results. In the first part, Kac's model will be introduced and its classic results will be discussed, in particular: relaxation towards equilibrium and derivation and solutions of the Boltzmann-Kac equation. After that the evolution of Kac's model will be studied, when in contact with a thermostat or with a thermal bath. Finally the recent attempts to extend the results to systems in contact with more than one thermostat or thermal bath initially at different temperatures, will be presented so as to arrive at a situation of actual non-equilibrium.		May, June 2021
Bonetto Federico ( bonetto@math.gatech.edu - Georgia Institute of Technology, Atlanta ) ⇧
PYTHON BASICS Python Basics Python Basics consists in a series of 8 lessons hosted at Dipartimento di Matematica e Fisica - Università degli Studi Roma TRE. The seminars will cover the fundamentals of Python, starting from the basics. A relevant of part of the seminars will be devoted to hands-on exercises, which we strongly recommend to the attendees. No prior knowledge of Python is required. Starting from really basic notions, the students will get acquainted with the standard programming techniques used in Python; moreover, to test the competences acquired by the students, the last 2 lessons will be devoted to the implementation of an actual problem that subsumes most of what has been explained during the lessons. A certificate of attendance will be issued to all participants.		semester I
Paola CELIO ( celio@fis.uniroma3.it - Universita degli Studi Roma TRE ) Corsi Pietro ( pietro.corsi@uniroma3.it - Universita degli Studi Roma TRE ) Sergio Augusto Barcelo Lins ( - Universita La Sapienza ) ⇧

IN OTHERS UNIVERSITIES ▾ ⇧

Institution
LA SAPIENZA - PHD SCHOOL IN MATHEMATICS
LA SAPIENZA - PHD SCHOOL IN MATHEMATICS FOR ENGINEERING
TOR VERGATA - PHD SCHOOL IN MATHEMATICS

ONLINE COURSEES IN OTHERS UNIVERSITIES ▾ N : 1 ⇧

Course name	Note	Period	Time Table
THE THEORY OF THE DEFECT AND ITS APPLICATION TO THE PROBLEM OF LOCAL UNIFORMIZATION The theory of the defect and its application to the problem of local uniformization Doctoral Program in Mathematical Science Univ. Padova, Dept Math "“Tullio Levi-Civita” Il 1oincontro sara' Venerdi' 19/2 alle ore 15, via zoom. Poi ci sara' un incontro a settimana, il Venerdi' mattina, sempre via zoom secondo questo calendario: 19 febbraio - ore 15:00-17:00 26 febbraio - ore 11:00-13:00 5 marzo - ore 11:30-13:00 12 marzo - ore 11:00-13:00 19 marzo - ore 11:00-13:00 26 marzo - ore 11:00-13:00 2 aprile - ore 11:00-13:00 9 aprile - ore 11:00-13:00 Per iscriversi: https://dottorato.math.unipd.it/current-activity/FutureActivities	THE THEORY OF THE DEFECT AND ITS APPLICATION TO THE PROBLEM OF LOCAL UNIFORMIZATION Corso di Dottorato di Matematica , Universita' di Padova	Feb-April, 2021
Franz-Viktor Kuhlmann ( - University of Szczecin, Poland ) ⇧