Dipartimento di Matematica -UTV-

Date	Type	Start	End	Room	Speaker	From	Title
14/11/23	Seminario	14:30	16:00	1101 D'Antoni	Ernesto Mistretta	Università di Padova	Vector Bundles, Parallelizable manifolds, Fundamental groups Abstract We will show how some basic questions about semiampleness of vector bundles can be interpreted in a geometric way. In particular we will distinguish between two non equivalent definitions of semiampless appearing in the literature, and give a geometric interpretation considering the holomorphic cotangent bundle. We will generalize these examples obtaining a biholomorphic characterisation of abelian varieties and their quotients (called hyperelliptic varieties). In order to achieve a similar biholomorphic characterisation of parallelizable compact complex manifolds and their quotients, we will consider another basic question about semiample vector bundles. Time permitting, we will conclude with a question on fundamental groups of manifolds with semiample cotangent bundle. Part of this work is in collaboration with Francesco Esposito.
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 Abstract 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 Abstract 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 Abstract 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 Abstract 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	Victor REINER	University of Minnesota	Colloquium di Dipartimento "Combinatorics of configuration spaces - recent progress" N.B.: This talk is part of the activity of the MIUR Excellence Department Project Mat-Mod@TOV (CUP E83C23000330006) Abstract 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 Abstract 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 Abstract 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	Misha FEIGIN	University of Glasgow	Algebra & Representation Theory Seminar (ARTS) "Quasi-invariants and free multi-arrangements" N.B.: This talk is part of the activity of the MIUR Excellence Department Project Mat-Mod@TOV (CUP E83C23000330006) Abstract 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	Luca FRANCONE	Université "Claude Bernard" Lyon 1	Algebra & Representation Theory Seminar (ARTS) "Minimal monomial lifting of cluster algebras and branching problems" N.B.: This talk is part of the activity of the MIUR Excellence Department Project Mat-Mod@TOV (CUP E83C23000330006) Abstract 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.