Offerta formativa erogata A.A. 2019/2020


 



Courses 2019-20



List of courses held by invited professors  (details below)



T. Schick - The topology of positive scalar curvature

M. Hauray - M. Pulvirenti - Scaling limits and effective equation in kinetic theory

C. De Concini - Hodge theory and matroids

D. Noja - Nonlinear Schroedinger equation on graphs

C. Bernardi, A. Cusi - Seminari di ricerca in didattica della matematica

P. Pragacz - Gysin formula for homogeneous spaces

G. Besson - Finiteness and compactness in negative curvature





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 (6 credits) - 24 hours


Maxime Hauray - Mario Pulvirenti

Scaling limits and effective equation in kinetic theory


Monday 15.30-17.30, Wednesday 14.00-16.00

First class: Monday 10 February 2020



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 (3 credits) - 12 hours



First lecture: Tue 4 February, Aula B 15:00-17:00




COURSE (3 credits) - 10 hours


Diego Noja

Nonlinear Schroedinger equation on graphs


Room B

Mon 27 Jan - at 16:00-18:00

Tue 28-Wed 29-Thu 30 Jan - at 14:00-16:00






Fri 31 Jan - at 10:00-12:00

 


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 e Annalisa Cusi; intervengono come docenti anche Alessandro Gambini, Marta Menghini, Nicoletta Lanciano, Enrico Rogora. 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.






 





PhD courses at Roma Tor Vergata and Roma Tre:



PhD courses at Roma "Tor Vergata"

PhD courses at Roma Tre





 




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