21/11/23  Seminario  14:30  16:00  1101 D'Antoni  Ruije Yang  Humboldt University, Berlin  The geometric RiemannSchottky problem and Hodge theory
It is a classical problem in algebraic geometry, dated back to Riemann, to characterize Jacobians of smooth projective curves among all principally polarized abelian varieties. In 2008, CasalainaMartin proposed a conjecture in terms of singularities of theta divisors. In this talk, I will present a partial solution of this conjecture using Hodge theory and Dmodules. We also show that this conjecture can be deduced from a conjecture of Pareschi and Popa on GV sheaves and minimal cohomology classes. 
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 DrinfeldYetter algebra"
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 DrinfeldYetter 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 treelike approach to linear infinity operads"
N.B.: This talk is part of the activity of the MIUR Excellence Department Project MatMod@TOV (CUP E83C23000330006)
Arisen in Algebraic Topology to model the uptohomotopy associative algebra structure of loop spaces, operads can be thought of as collections of *spaces* of nary operations together with composition laws between them. We talk about oooperads when these operations can be composed only 'uptohomotopy'. When the nary operations organise into actual topological spaces/simplicial sets, several equivalent models for the homotopy theory of oooperads have been developed. Of our interest is Weiss and Moerdijk's approach, where a certain category of trees replaces the simplex category, and oocategorical 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 oooperads enriched in chain complexes ('linear'). In this talk, we explain how the treelike approach can be applied to the linear case. We discuss the combinatorics of trees and a Segallike condition which allows to define linear oooperads as certain coalgebras over a comonad. Then, by considering a category of 'trees with partitions', we realize linear oooperads 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.
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
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
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 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  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 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)
