Dipartimento di Matematica -UTV-

Date	Type	Start	End	Room	Speaker	From	Title
17/11/23	Seminario	16:00	17:00	1201 Dal Passo	Andrea RIVEZZI	Università di Milano "Bicocca"	Algebra & Representation Theory Seminar (ARTS) "Universal quantizations and the Drinfeld-Yetter algebra" Abstract In a renowned series of papers, Etingof and Kazhdan proved that every Lie bialgebra can be quantized, answering positively a question posed by Drinfeld in 1992. The quantization is explicit and "universal", that is it is natural with respect to morphisms of Lie bialgebras. A cohomological construction of universal quantizations has been later obtained by Enriquez, relying on the coHochschild complex of a somewhat mysterious cosimplicial algebra. In this talk, I will review the realization of Enriquez' algebra in terms of "universal endomorphisms" of a Drinfeld-Yetter module over a Lie bialgebra, due to Appel and Toledano Laredo, and present a novel combinatorial description of its algebra structure. This is a joint work with A. Appel.
17/11/23	Seminario	14:30	15:30	1201 Dal Passo	Francesca PRATALI	Université Sorbonne - Paris Nord	Algebra & Representation Theory Seminar (ARTS) "A tree-like approach to linear infinity operads" N.B.: This talk is part of the activity of the MIUR Excellence Department Project Mat-Mod@TOV (CUP E83C23000330006) Abstract Arisen in Algebraic Topology to model the up-to-homotopy associative algebra structure of loop spaces, operads can be thought of as collections of spaces of n-ary operations together with composition laws between them. We talk about oo-operads when these operations can be composed only 'up-to-homotopy'. When the n-ary operations organise into actual topological spaces/simplicial sets, several equivalent models for the homotopy theory of oo-operads have been developed. Of our interest is Weiss and Moerdijk's approach, where a certain category of trees replaces the simplex category, and oo-categorical methods are generalized to the operadic context. However, while the theory is well developed in the topological case, very little is known for what it concerns oo-operads enriched in chain complexes ('linear'). In this talk, we explain how the tree-like approach can be applied to the linear case. We discuss the combinatorics of trees and a Segal-like condition which allows to define linear oo-operads as certain coalgebras over a comonad. Then, by considering a category of 'trees with partitions', we realize linear oo-operads as a full subcategory of a functor category
15/11/23	Seminario	15:00	16:30	1101 D'Antoni	Lorenza Guerra	U Roma Tor Vergata	On the mod p cohomology of complete unordered flag manifolds in C^n and R^n. Abstract Flag manifolds are topological spaces parametrizing nested subspaces in a fixed vector space. On the complete flag manifold of C^n and R^n there is a natural action of the symmetric group on n letters. In this talk I will describe the cohomology of the quotient space of this action with coefficients in prime fields of positive characteristic. After recalling the basic definitions and providing some motivation, I will recall some algebraic and combinatorial properties of the cohomology of extended symmetric powers of topological spaces. I will then apply them to the classifying spaces of wreath products and use some spectral sequence argument to determine the desired cohomology. If enough time remains, I will briefly hint at a connection with E_n operads and Atiyah and Sutcliffe’s conjecture on the geometry of point particles.
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.