Seminari/Colloquia
Pagina 12
Date  Type  Start  End  Room  Speaker  From  Title 

24/11/23  Seminario  16:00  17:00  1201 Dal Passo  Frank Neumann  U Pavia  Preludes to the EilenbergMoore and the LeraySerre spectral sequences
The LeraySerre and the EilenbergMoore spectral sequence are fundamental tools in algebraic topology for computing cohomology. We describe the relationship between these two spectral sequences when both of them share the same abutment. There exists a joint trigraded refinement of the LeraySerre and the EilenbergMoore spectral sequence. This refinement involves two more spectral sequences which abut to the initial terms of the LeraySerre and the EilenbergMoore spectral sequence, respectively. We show that one of these always degenerates from its second page on and that the other one satisfies a localtoglobal property: it degenerates for all possible base spaces if and only if it does so when the base space is contractible. When the preludes degenerate early enough, they appear to echo Deligne's decalage machinery, but in general, this is an illusion. We will discuss several principal fibrations to illustrate the possible cases and give applications, in particular, to Lie groups, group extensions, and torus bundles.
This talk is part of the activity of the MIUR Excellence Department Project MatMod@TOV (CUP E83C23000330006).

24/11/23  Seminario  14:30  15:30  1201 Dal Passo  Roberto Pagaria  U Bologna  Cohomology ring of arrangement complements
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 OrlikSolomon theorem (1980). Then, we describe the real case and the GelfandVarchenko 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 OrlikSolomon and De ConciniProcesi relations from the GelfandVarchenko 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 MatMod@TOV (CUP E83C23000330006).

22/11/23  Seminario  16:00  17:00  1201 Dal Passo  Yuto Moriwaki  Riken (Wako, Japan)  Operator product expansion in two dimension conformal field theory
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 twodimensional 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 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  "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  "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.

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