Seminari/Colloquia
Pagina 13
Date  Type  Start  End  Room  Speaker  From  Title 

06/11/23  Seminario  16:00  17:00  1201 Dal Passo  Alessio Bottini  Università Roma Tor Vergata & Université ParisSaclay  Stable sheaves on hyperKähler manifolds
The only known examples of hyperKähler manifolds are constructed from moduli spaces of sheaves on symplectic surfaces. One would expect that moduli spaces of sheaves on hyperKähler manifolds should be themselves hyperKähler, but they have proven much more challenging to study. In this talk, I will describe an instance where such an analysis is possible on a fourdimensional manifold. In this case, the moduli space is indeed a hyperKähler manifold of dimension 10, deformation equivalent to O'Grady's example.

06/11/23  Seminario  14:30  16:00  1101 D'Antoni  Claire Voisin  Institut de Mathématiques de JussieuParis rive gauche  On the smoothing problem for cycles in the Whitney range
Borel and Haefliger asked whether the group of cycle classes on a smooth projective variety X is generated by classes of smooth subvarieties (such cycle classes will be said "smoothable"). Outside the Whitney range, that is, when the codimension c of the cycles is not greater than the dimension d, there are many counterexamples, the most recent ones being due to Olivier Benoist. In the Whitney range where c>d, it is known that (c1)!z is smoothable for any cycle z of dimension d. Also Hironaka proved that cycles of dimension at most 3 are smoothable.
I study the cycles obtained by pushingforward products of divisors under a flat projective map from a smooth variety. I show they are smoothable in the Whitney range and I conjecture that any cycle can be constructed this way. I prove that, for any cycle z of dimension d, (d6)!z can be constructed this way, which implies that (d6)!z is smoothable if d

03/11/23  Colloquium  16:00  17:00  1201 Dal Passo  "Combinatorics of configuration spaces  recent progress" N.B.: This talk is part of the activity of the MIUR Excellence Department Project MatMod@TOV (CUP E83C23000330006)
The topology of the space of n distinct labeled points in Euclidean space has a long history. Its cohomology is fairly well understood, including as a representation of the symmetric group permuting the n labels. These representations also have mysterious connections with combinatorial notions like descents of permutations, and sometimes "hidden" actions of the symmetric group on n+1 points. We will discuss several results in recent years elucidating some of these connections, including work by and with Marcelo Aguiar, Ayah Almousa, Sarah Brauner, Nick Early, and Sheila Sundaram.
Note: This talk is part of the activity of the MIUR Excellence Department Project MatMod@TOV (CUP E83C23000330006)  
31/10/23  Seminario  14:30  16:00  1101 D'Antoni  Benjamin Wesolowski  ENS de Lyon  The supersingular Endomorphism Ring and One Endomorphism problems are equivalent
The supersingular Endomorphism Ring problem is the following: given a supersingular elliptic curve, compute all of its endo morphisms. The presumed hardness of this problem is foundational for isogenybased cryptography. The One Endomorphism problem only asks to find a single nonscalar endomorphism. We prove that these two problems are equivalent, under probabilistic polynomial time reductions. We prove a number of consequences: on the security of cryptosystems, on the hardness of computing isogenies between supersingular elliptic curves, and on solving the endomorphism ring problem.

24/10/23  Seminario  14:30  16:00  1101 D'Antoni  Thomas Krämer  Humboldt University  Arithmetic finiteness of very irregular varieties
We prove the Shafarevich conjecture for a large class of irregular varieties. Our proof relies on the LawrenceVenkatesh method as used by LawrenceSawin, together with the big monodromy criterion from our previous work with Javanpeykar, Lehn and Maculan. This is joint work in progress with Marco Maculan (IMJ Paris).

20/10/23  Seminario  16:00  17:00  1201 Dal Passo  "Quasiinvariants and free multiarrangements" N.B.: This talk is part of the activity of the MIUR Excellence Department Project MatMod@TOV (CUP E83C23000330006)
Quasiinvariants are special polynomials associated with a finite reflection group W and a multiplicity function. They appeared in 1990 in the study of CalogeroMoser integrable systems by Chalykh and Veselov, in which case they are the highest symbols of differential operators which form a large commutative ring. Similarly to all the polynomials, quasiinvariants form a free module over invariant polynomials of rank W, and they have other good properties. Quasiinvariants form representations of spherical Cherednik algebras as was established by Berest, Etingof and Ginzburg in 2003, which gives a way to establish the freeness property. I am going to explain a more recent application of quasiinvariants to the theory of free multiarrangements of hyperplanes. In this case one is interested in the module of logarithmic vector fields which is known to be free over polynomials for some arrangements including Coxeter ones. Quasiinvariants can be used to construct elements of this module, and they also lead to new free multiarrangements in the case of complex reflection groups.
The talk is based on a joint work with T. Abe, N. Enomoto and M. Yoshinaga.  
20/10/23  Seminario  14:30  15:30  1201 Dal Passo  "Minimal monomial lifting of cluster algebras and branching problems" N.B.: This talk is part of the activity of the MIUR Excellence Department Project MatMod@TOV (CUP E83C23000330006)
We will talk about minimal monomial lifting of cluster algebras. That is sort of a homogenisation technique, whose goal is to identify a cluster algebra structure on some schemes "suitable for lifting", compatibly with a base cluster algebra structure on a given subscheme. We will see how to apply this technique to study some branching problems, in representation theory of complex reductive groups and, time permitting, we will discuss some possible development as the construction of polyhedral models for multiplicities.
 
18/10/23  Seminario  16:00  17:00  2001  Valerio Proietti  University of Oslo  Nonlocal games and Grothendieck's inequalities
I will explore some recent results based on the interaction of operator space theory and quantum nonlocality. In particular I will emphasize the connection between large violations of Bell inequalities and certain norms in Banach and operator space categories. Finally, using Grothendieck's inequality, I will derive some interesting consequences for the parallel repetition problem in the context of XOR games.

17/10/23  Seminario  14:30  16:00  1101 D'Antoni  Andrea Bruno  Roma 3  On Syzygy schemes
If X is a projective variety cut out byquadrics, the p^th Syzygy scheme Syz_p(X) is the scheme cut out by quadrics involved in a p^th syzygy of X, and it turns out to capture refined geometrical properties of X in its embedding.
We report on joint work in progress with M. Aprodu and E. Sernesi, concerning the second Syzygy scheme Syz_2(C) of a smooth curve in case C is embedded either by the canonical line bundle or by a nonspecial line bundle L, aiming at a classification of all (C,L) such that Syz_2(C) strictly contains

06/10/23  Seminario  16:00  17:00  1201 Dal Passo  "Operator Algebras That One Can See"
Many wellknown examples of "noncommutative spaces", like Woronowicz' quantum SU(2) or VaksmanSoibelman odddimensional quantum spheres, can be described by C*algebras associated to directed graphs. More generally, many compact quantum groups and quantum homogeneous spaces, can be described by convolution C*algebras of "nice" groupoids. C*algebras associated to combinatorial data (graphs, diagrams, groupoids) allow efficient models to attack key open problems in noncommutative geometry.
The aim of this talk is to present some basic ideas of noncommutative geometry, using graph and groupoid C*algebras as examples of "noncommutative spaces that one can see". 
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