Offerta formativa erogata


Courses 2019-20

List of courses held by invited professors (details below)

T. Schick - The topology of positive scalar curvature
S. Doplicher - Operator algebras
M. Pulvirenti - Scaling limits and effective equation in kinetic theory
D. Noja - Nonlinear Schroedinger equation on graphs
C. Bernardi - Seminari di ricerca in didattica della matematica
P. Pragacz - Gysin formula for homogeneous spaces
G. Besson - Finiteness and compactness in negative curvature
C. De Concini - To be announced

List of graduate courses (in common with Laurea Magistrale)
Details here and here

Fall term

ISTITUZIONI DI ALGEBRA SUPERIORE - MAT/02

ALGEBRA SUPERIORE - MAT/02

ISTITUZIONI DI GEOMETRIA SUPERIORE - MAT/03

TOPOLOGIA ALGEBRICA - MAT/03

GEOMETRIA RIEMANNIANA - MAT/03

CORSO MONOGRAFICO DI STORIA DELLA MATEMATICA - MAT/04

ISTITUZIONI DI ANALISI SUPERIORE - MAT/05

EQUAZIONI ALLE DERIVATE PARZIALI - MAT/05

EQUAZIONI DIFFERENZIALI NON LINEARI - MAT/05

PROCESSI STOCASTICI - MAT/06

STATISTICA MATEMATICA - MAT/06

CALCOLO STOCASTICO E APPLICAZIONI - MAT/06

FISICA MATEMATICA SUPERIORE - MAT/07

ANALISI DI SEQUENZE DI DATI - MAT/07

MECCANICA DEI FLUIDI - MAT/07

MODELLI DI RETI NEURALI - MAT/07

ISTITUZIONI DI ANALISI NUMERICA - MAT/08

FISICA MODERNA - FIS/08

TEORIA DEGLI AUTOMI - INF/01

TEORIA DEI CODICI - INF/01

METODI NUMERICI PER LE EQUAZIONI ALLE DERIVATE PARZIALI NON LINEARI - ING-IND/06


Spring term

MATEMATICA DISCRETA - MAT/02

GEOMETRIA ALGEBRICA - MAT/03

GEOMETRIA SUPERIORE - MAT/03

MATEMATICHE ELEMENTARI DA UN PUNTO DI VISTA SUPERIORE - MAT/03

FONDAMENTI DELLA MATEMATICA - MAT/04

DIDATTICA DELLA MATEMATICA - MAT/04

SPAZIO E FORMA - MAT/04

ANALISI FUNZIONALE - MAT/05

ANALISI SUPERIORE - MAT/05

MODELLI ANALITICI PER LE APPLICAZIONI - MAT/05

ISTITUZIONI DI PROBABILITA' - MAT/06

ISTITUZIONI DI FISICA MATEMATICA - MAT/07

SISTEMI DINAMICI - MAT/07

METODI NUMERICI PER LE EQUAZIONI ALLE DERIVATE PARZIALI - MAT/08

ELEMENTI DI FISICA TEORICA - FIS/02

TEORIA DEGLI ALGORITMI - INF/01




Courses held at the department of Mathematics at the school of engineering (SBAI)

Details here 



Reading courses

Here is a list of potential reading courses by the faculty and of some reading courses held in the previous years. Graduate students are encouraged to contact faculty members and request the activation of reading courses of their interest.


Examination report


Abstracts and details
 

COURSE (4 credits) - 16 hours
Thomas Schick

Dates: April 2020 (to be determined)


COURSE (8 credits) - (to be activated upon request)
Sergio Doplicher
Operator algebras

Dates: to be determined 

COURSE (4 credits) - 16 hours
Mario Pulvirenti
Scaling limits and effective equation in kinetic theory

Dates: to be announced

Abstract. In this course I will discuss the scaling limits necessary to outline the physical regimes one wants to discuss, starting from  large (classical) particle systems. The goal is to derive rigorously the effective equations which are largely used in kinetic theory, as the Boltzmann, Vlasov and Landau equations. From a mathematical side we have very few results and many open challenging problems.

COURSE (4 credits) - 10 hours
Diego Noja
Nonlinear Schroedinger equation on graphs

Dates: second half of January 2020
 
CORSO (8 crediti)
Seminari di ricerca in didattica della matematica
Giovedì, 15:00-17:30 in Aula B - Calendario degli incontri

Il corso, che si articola in seminari in parte indipendenti fra loro, si propone di offrire un panorama di alcune tematiche di ricerca in didattica della matematica. Fra i temi che saranno affrontati, citiamo: aspetti legati alla dimostrazione (sviluppo di argomentazioni, vari stili di dimostrazione, ecc.), l'evoluzione del concetto di matematiche elementari da un punto di vista superiore, le concezioni iniziali degli studenti, il passaggio dalla scuola secondaria all’università. 

Il corso è coordinato da Claudio Bernardi; intervengono come docenti anche Annalisa Cusi, Alessandro Gambini, Marta Menghini, Nicoletta Lanciano. Saranno inoltre occasionalmente invitati docenti di altre università italiane.
 

COURSE
Gysin formula for homogeneous spaces
Piotr Pragacz (Polish Academy of Sciences)

Lectures
1. Flag bundles, Segre polynomials, and push-forwards
Wed 13 November, 14:00-15:00, Sala di Consiglio

We give Gysin formulas for all flag bundles of types A, B, C, D. The formulas (and also the proofs) involve only the Segre classes of the original vector bundles and characteristic classes of universal bundles. As an application we provide new determinantal formulas.
This is a joint work with Lionel Darondeau.
 
2.-3. Gysin maps, duality, and Schubert classes I-II
Thu 14 and Mon 18 November, 15:00-16:00, Room B
 
We establish a Gysin formula for Kempf-Laksov flag bundles and we prove a duality theorem for Grassmann
bundles. We then combine them to study Schubert bundles, their push-forwards and fundamental classes.
This is a joint work with Lionel Darondeau.
 
4. A Gysin formula for Hall-Littlewood polynomials
Thu 21 November, 15:00-16:00, Room B
 
We give a formula for pushing forward the classes of Hall-Littlewood polynomials in Grassmann bundles, generalizing Gysin formulas for Schur S-  and P -functions.
 

COURSE
Finiteness and Compactness in Negative Curvature
Gérard Besson (Grenoble)

Lectures: 1, 3, 8, 10 October 2019 - Room B, 14:00-17:00

Abstract
Finiteness and compactness problems in Riemannian geometry date back to the pioneering works of Cheeger, Gromov, Grove-Petersen, Anderson et al. ([C],[G],[GP],[A]) which started the ``theory of convergence of Riemannian manifolds'', one of the main trends in Riemannian geometry and topology as of today. 

The aim of the course is to generalize, in negative curvature, the classical works of Cheeger and Gromov under much weaker assumptions. 
Actually, the classical bounds on sectional/Ricci curvature and on the injectivity radius are replaced, in our setting, only by a bound on the entropy, which is a much more flexible (and global) invariant. Morover, by "negative curvature" we mean Gromov-hyperbolicity, which is a substitute of classical Riemannian negative sectional curvature on large-scale. This allows us to consider larger classes of spaces (not only Riemannian manifolds) and to better characterize the limit spaces. At present, the more refined results of convergence theory apply only to classes of manifolds with a lower bound on the Ricci curvature, without any control of the regularity (and dimension) of the arising limit spaces.
The main topics touched in the course will be:
-a Margulis' lemma for groups acting on Gromov-hyperbolic spaces;
-a Bishop-Gromov inequality for Gromov-hyperbolic spaces;
-estimates of the first Betti numbers for quotients of Gromov-hyperbolic spaces;
-finiteness and compactness theorems. 
 
The course will be based on the joint works (partly in progress) with G.Courtois, S.Gallot and A.Sambusetti: 
[BCGS] G.Besson, G.Courtois, S.Gallot, A.Sambusetti, Curvature-free Margulis lemma for Gromov-Hyperbolic spaces, preprint arxiv: 1712.08386 (2017)
[BCGS2] G.Besson, G.Courtois, S.Gallot, A.Sambusetti, Finiteness and compactness for Gromov-Hyperbolic spaces, in preparation.







Courses 2018-19


COURSE
The hard Lefschetz theorem beyond positivity, and applications to combinatorics

Karim Adiprasito (Jerusalem)
Lectures: 15-24 April 2019, Room B, 10:00-12:30

COURSE  (10 hours)
Conservation laws and fractional BV spaces
Stephane Junca (Nice)
First meeting: Thursday 2 May, Room B, 16:00-18:00

COURSE (16 hours, possibly +16 hours)
Geometric methods in representation theory of finite dimensional algebras

Giovanni Cerulli Irelli (SBAI)
Lectures: Tuesday at 10:00 in Room B
Beginning 15 January 2019

COURSE  (30 hours)
Moduli spaces
Eduardo Esteves (IMPA)
Location: Department of Mathematics of Roma 3
Beginning: 18 October 2018 (Roma 3 - Room 311 - at 11:00)

COURSE
Metric Geometry and Curvature of Domains in Cn
Hervé Gaussier (Institut Fourier - Grenoble)
Lectures 1-4: Wednesday 15:00-17:30 (Aula Dal Passo, Dipartimento di Matematica Univ. Roma “Tor Vergata")
First meeting: Wednesday 14 November 2018
Topics: generalities on metric spaces, Gromov hyperbolic spaces, curvature of Kähler metrics

COURSE (15+15 hours, Nov 2018-Jan 2019)
Non-local operators of convolution type. Homogenization and some asymptotic properties.
Andrey Piatnitski (The Arctic University of Norway e Russian Academy of Science)
Lectures: Tuesday, 14:00 (Aula Dal Passo, Dipartimento di Matematica Univ. di Roma "Tor Vergata")
First meeting: Tuesday 13 November 2018

COURSE (16 hours)
Tecniche di biforcazione in problemi variazionali geometrici (scaletta del corso)
Paolo Piccione
 (Universidade de São Paulo)
Lectures: Monday and Thursday, 10:00-13:00 in Room B
First lecture: 7 January 2019 - Last lecture: 24 January 2019

COURSE (15 lectures, 30 hours)
Meccanica quantistica
Sergio Doplicher ("Sapienza" Università di Roma)
Period: 8 January - 8 February 2019, Tue-Wed-Fri 12:00-14:00 in Room B

COURSE  (12 lectures, 24 hours)
The dimer model: equilibrium and non-equilibrium aspects
Fabio Toninelli (CNRS - ICJ Lyon 1)
First lecture: Monday 1 Aprile 2019 - Room B, 10:30-13:00 

 

Reading courses 2018-19

Seminar on geometric measure theory

  • Teacher: E. Spadaro
  • Beginning: February 2019
  • When/where: Monday 15:30, Room B
Geometric methods in representation theory of finite dimensional algebras

Cherednik Double Affine Hecke Algebra

  • Teacher: P. Bravi
  • Beginning: TBA
  • When/where: TBA

Forma di Wulff in meccanica statistica

  • Teacher: L. Bertini et al.
  • When/where: first meeting Wed 7 November, Room B at 11-13 - then weekly meetings (Nov-Dec 2018)

Scopo del corso: capire come funziona la teoria della forma di Wulff in meccanica statistica di equilibrio.

In particolare vorremmo studiare alcuni risultati fine anni '90 di Cerf e Bodineau ottenuti utilizzando tecniche probabilistiche e strumenti di teoria geometrica della misura che descrivono le configurazioni tipiche del modello di Ising (microscopico) in termini di un problema variazionale macroscopico detto forma di Wulff (=problema isoperimetrico con tensione superficiale non isotropa).
Il programma del primo incontro (7 novembre) prevede una breve introduzione alla meccanica statistica, l'introduzione del modello di Ising e la corrispondente transizione di fase.
 
Cerf, R. The Wulff crystal in Ising and percolation models. Lectures from the 34th Summer School on Probability Theory held in Saint-Flour, Lecture Notes in Mathematics, 1878.


Corsi della Laurea Magistrale 2018-19

A.A 2018-19, primo semestre

Geometria riemanniana, teacher: S. Diverio
Algebra superiore
, teacher: C. Malvenuto

A.A 2018-19, secondo semestre

Geometria algebrica, teacher: K. O'Grady
Geometria superiore
, teacher: D. Fiorenza

 


PhD courses at Roma Tor Vergata and Roma Tre:

PhD courses at Roma "Tor Vergata"
PhD courses at Roma Tre


 

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