Pagina 15

Date | Type | Start | End | Room | Speaker | From | Title |
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07/11/23 | Seminario | 15:00 | 16:00 | 1101 D'Antoni | Anne Moreau | Laboratoire de Mathématiques d'Orsay | Functorial constructions of double Poisson vertex algebras
To any double Poisson algebra we produce a double Poisson vertex algebra using the jet algebra construction. We show that this construction is compatible with the representation functor which associates to any double Poisson (vertex) algebra and any positive integer a Poisson (vertex) algebra. We also consider related constructions, such as Poisson and Hamiltonian reductions. This allows us to provide various interesting examples of double Poisson vertex algebras, in particular from double quivers. This is a joint work with Tristan Bozec and Maxime Fairon. |

07/11/23 | Seminario | 14:00 | 15:00 | 1101 D'Antoni | Emanuele Macrì | Laboratoire de Mathematiques d'Orsay | Deformations of stability conditions Bridgeland stability conditions have been introduced about 20 years ago, with motivations both from algebraic geometry, representation theory and physics.
One of the fundamental problem is that we currently lack methods to construct and study such stability conditions in full generality.
In this talk I would present a new technique to construct stability conditions by deformations, based on joint works with Li, Perry, Stellari and Zhao.
As application, we can construct stability conditions on very general abelian varieties and deformations of Hilbert schemes of points on K3 surfaces. |

06/11/23 | Seminario | 16:00 | 17:00 | 1201 Dal Passo | Alessio Bottini | Università Roma Tor Vergata & Université Paris-Saclay | Stable sheaves on hyper-Kähler manifolds The only known examples of hyper-Kähler manifolds are constructed from moduli spaces of sheaves on symplectic surfaces. One would expect that moduli spaces of sheaves on hyper-Kähler manifolds should be themselves hyper-Kähler, 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 four-dimensional manifold. In this case, the moduli space is indeed a hyper-Kähler 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 Jussieu-Paris 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 (c-1)!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 pushing-forward 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, (d-6)!z can be constructed this way, which implies that (d-6)!z is smoothable if d |

03/11/23 | Colloquium | 16:00 | 17:00 | 1201 Dal Passo | University of Minnesota | Colloquium di Dipartimento "Combinatorics of configuration spaces - recent progress"
This talk is part of the activity of the MIUR Excellence Department Project Mat-Mod@TOV (CUP E83C23000330006) N.B.: 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 Mat-Mod@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 isogeny-based cryptography. The One Endomorphism problem only asks to find a single non-scalar 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 Lawrence-Venkatesh method as used by Lawrence-Sawin, 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 | University of Glasgow | Algebra & Representation Theory Seminar (ARTS) "Quasi-invariants and free multi-arrangements"
This talk is part of the activity of the MIUR Excellence Department Project Mat-Mod@TOV (CUP E83C23000330006) N.B.: Quasi-invariants are special polynomials associated with a finite reflection group W and a multiplicity function. They appeared in 1990 in the study of Calogero-Moser 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, quasi-invariants form a free module over invariant polynomials of rank |W|, and they have other good properties. Quasi-invariants 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 quasi-invariants to the theory of free multi-arrangements 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. Quasi-invariants can be used to construct elements of this module, and they also lead to new free multi-arrangements 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 | Université "Claude Bernard" Lyon 1 | Algebra & Representation Theory Seminar (ARTS) "Minimal monomial lifting of cluster algebras and branching problems"
This talk is part of the activity of the MIUR Excellence Department Project Mat-Mod@TOV (CUP E83C23000330006) N.B.: 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 |
Seminario di Algebre di Operatori
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. |

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