Dipartimento di Matematica -UTV-

Date	Type	Start	End	Room	Speaker	From	Title
24/11/23	Seminario	14:30	15:30	1201 Dal Passo	Roberto Pagaria	U Bologna	Cohomology ring of arrangement complements Abstract The aim of this talk is to provide a uniform and intuitive description of the cohomology ring of arrangement complements. We introduce complex hyperplane arrangements and state the Orlik-Solomon theorem (1980). Then, we describe the real case and the Gelfand-Varchenko ring (1987). We define toric arrangements and present their cohomology ring (De Concini, Procesi (2005) and Callegaro, D'Adderio, Delucchi, Migliorini, and P. (2020)). Finally, we show a new technique to prove the Orlik-Solomon and De Concini-Procesi relations from the Gelfand-Varchenko ring. The technique applied to abelian arrangements provides a presentation of their cohomology. This is work in progress with Evienia Bazzocchi and Maddalena Pismataro. This talk is part of the activity of the MIUR Excellence Department Project Mat-Mod@TOV (CUP E83C23000330006).
22/11/23	Seminario	16:00	17:00	1201 Dal Passo	Yuto Moriwaki	Riken (Wako, Japan)	Operator algebras seminar Operator product expansion in two dimension conformal field theory Abstract Conformal field theory can be defined using the associativity and the commutativity of the product of quantum fields (operator product expansion). An important difference between conformal field theory and classical commutative associative algebra is "the divergence" arising from the product of quantum fields, a difficulty that appears in quantum field theory in general. In this talk we will explain that in the two-dimensional case this algebra can be controlled by "the representation theory" of a vertex operator algebra and that the convergence of quantum fields is described by the operad structure of the configuration space.
21/11/23	Seminario	14:30	16:00	1101 D'Antoni	Ruije Yang	Humboldt University, Berlin	The geometric Riemann-Schottky problem and Hodge theory Abstract 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, Casalaina-Martin 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 D-modules. 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 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.