9:00-9:40
Giovanna Andreucci

Titolo: ON THE NONLINEAR THIN OBSTACLE PROBLEM
 
Abstract: The thin obstacle problem or n-dimensional Signorini problem is a classical variational problem arising
in several applications, starting with its first introduction in elasticity theory. The vast literature concerns mostly
quadratic energies, whereas only partial results have been proved in the nonlinear case. In this seminar we consider
the thin boundary obstacle problem for a general class of nonlineraities and we prove the optimal C^{1,1/2}-regularity
of the solutions in any space dimension.
 
9:45 - 10:25
Andrea Drago

Titolo: VOLUME ENTROPY AS A LARGE SCALE ANALOGUE OF NEGATIVE CURVATURE

Abstract: The interplay between metric and topology has been explored for more than a century, and has driven
mathematical research in various fields. A classical example of this relationship is given by the Uniformization Theorem
of closed surfaces. For more general manifolds such a complete classification is out of reach, but there are many
results that describe how constraints on the metric impose constraints on the topology, and vice versa. We will focus
on the negative curvature setting, where the topology is more complex, from a metric perspective. After reviewing some
classical theorems we will define a volume entropy as the asymptotic exponential growth rate of the volume of balls in
the universal cover with respect to their radius. This quantity can be thought of as a mean, asymptotic version of the
Ricci curvature, so we will outline some the entropy analogues of the classical theorem, showing how the entropy can be
a measure of the topological complexity.
In the end there will be space for one final remark regarding the climate crisis, and the role of our research in such a key
moment of history.

10:45 - 11:25
Azzurra Ciliberti

Titolo: CATEGORIFICATION OF CLUSTER ALGEBRAS OF TYPE B AND C THROUGH SYMMETRIC QUIVERS

Abstract: After recalling the combinatorial definition by generators and relations of cluster algebras of type A, B and C,
we will state a cluster expansion formula for cluster algebras of type B and C in terms of cluster variables of type A.
Then, we will explain how to associate a symmetric quiver Q to any cluster of a cluster algebra of type B and C. Under
this correspondence, cluster variables of type B (resp. C) correspond to orthogonal (resp. symplectic) indecomposable
representations of Q.

11:30 - 12:10
Giacomo Hermes Ferraro

Titolo: SERIE ALLA EISENSTEIN NEI MODULI DI DRINFELD

abstract: La teoria dei moduli di Drinfeld, sviluppata da Anderson e Thakur negli anni 90, è concepibile come un analogo
in caratteristica finita della teoria delle curve ellittiche di variabile complessa, dove il ruolo dell'anello degli interi Z è
svolto dall'anello delle funzioni regolari di una curva proiettiva liscia X/F_q fuori da un punto razionale \infty.
Le somme di Gauss-Thakur, analogo delle somme di Gauss, sono interpolate da cosiddette "funzioni speciali", funzioni
analitiche su un cambio base di X\setminus\infty. In questa presentazione, parlerò della relazione di queste funzioni con
serie "alla Eisenstein", e ne esplorerò il significato.

12:15 - 12:55
Luca Casarin

Titolo: FACTORIZATION STRUCTURES AND A FACTORIZABLE FEIGIN-FRENKEL THEOREM

Abstract: The talk will be divided into two main parts. In the first one I will introduce the concept of a factorization
structure on a vector bundle on a manifold. This is a rather recent notion which applies in several geometric contexts
and sheaf theories and through time has found connections to the representation theory of quantum groups, the theory
of chiral algebras (a geometric version of the theory of vertex algebras) and last but not least the notion of an E_n algebra
in homotopical contexts. In the second part we will then move to discuss the Feigin-Frenkel theorem about the center of
the enveloping algebra of the affine algebra at the critical level and a factorization (in the above sense) version of it
which was part of my PhD project.
 
13:00 - 13:40
Matteo Micheli

Titolo: A SYMPLECTIC PROBLEM ON SPECIAL QUIVER GRASSMANNIANS

In this talk we will review the basics on quiver Grassmannians, and study a family of projective varieties with some very
good properties. Then we consider subvarieties defined by symplectic conditions, and see which of those properties still
hold true for the subvarieties.

CORSO
 
Title: Riemannian Holonomy Groups - docente Lorenzo Foscolo

Course Description:
The course will be an introduction to the theory of Riemannian holonomy groups and the geometry of manifolds
with special holonomy. After an introduction to holonomy and Berger’s classification of holonomy groups of irreducible
non-symmetric Riemannian manifolds, we will concentrate on the Ricci-flat holonomy groups. The second part of the
course will focus on constructions of complete non-compact and compact Ricci-flat manifolds with special and exceptional
holonomy.

Rough outline of the lecture contents:

1. Berger’s classification of the Riemannian holonomy groups. (Principal bundles and connections, the Levi-Civita
connection, parallel transport, Berger’s classification.)
2. The Ricci-flat holonomy groups. (Calabi-Yau, hyperkähler, G2 and Spin(7) metrics, Ricci-curvature and topology,
structure results for Ricci-flat manifolds.)
3. Kähler Ricci-flat metrics. (Kähler and complex geometry, the Calabi Conjecture, compact Calabi-Yau and hyperkähler
manifolds, moduli spaces.)
4. Examples of complete non-compact manifolds with special holonomy. (ALE hyperkähler 4-manifolds, the Calabi
Ansatz, Bryant-Salamon’s asymptotically conical manifolds with exceptional holonomy.)
5. Kummer-type constructions of compact manifolds with special holonomy. (The Kummer construction of hyperkähler
metrics on the K3 surface and generalisations.)

 - Recommended reading: a good reference for the course is D. Joyce, Compact manifolds with special holonomy. 
Oxford University Press, Oxford, 2000.
Schematic lecture notes are available at http://www.homepages.ucl.ac.uk/~ucahlfo/Holonomy2022.pdf 

- Date e orari: 4/5/18/19/25 giugno, 9.30-13.30, in Aula B e su Zoom:
https://uniroma1.zoom.us/j/87880328133?pwd=ZvcpXPihfzL1pSbtuyM0wRHH9lYDQb.1

 
 CORSO 

Title: " Introduction to stochastic partial differential equations", S. Cerrai  - Aula B - Bertini Lorenzo

- mercoledì 5 giugno  14:00 -16:00
- giovedì     6 giugno  10:00 -12:00
- martedì   18 giugno  14:00 -16:00
- giovedì    20 giugno 10:00 -12:00
- martedì   25 giugno  14:00 -16:00
- giovedì   27 giugno  10:00 -12:00