This is the third edition of an annual meeting whose main subject is the interaction between Algebra and Geometry, including topics such as: Representation Theory, Lie Theory, Poisson Geometry, Mathematical Physics, among others. The first meeting was held at IME-USP in 2015, followed by the second edition held at IMECC-UNICAMP as part of the II Brazilian Congress of Young Researchers in Pure and Applied Mathematics in 2016.

The talks will take place in Auditorio Jacy Monteiro of the Institute of Mathematics and Statistics of the University of Sao Paulo.

Program

Thursday, November 30

14:00-14:50

Speaker: Nicola Sambonet - IME-USP
Title: “Covering groups of minimal exponents"
Abstract: It is a common practice to mark the birth of group cohomology with the discovery of Hopf’s formula, since this formula has firstly related algebraic topology and representation theory of finite groups. In this context, the covering groups, which are the finite central extensions with the projective lifting property, are of fundamental importance, and those of minimal order are the well-known Schur’s covers. We will show that a suitable modification of Hopf’s formula produces covering groups of minimal exponent.

15:00-15:50
Speaker: Cristian Cárdenas - IME-USP
Title: “A geometric approach to rigidity of Lie groups, Lie subgroups and Lie group morphisms"
Abstract: In this talk we show how to use a Moser’s path method to produce geometric proofs to the questions of rigidity of Lie groups, Lie subgroups, and Lie group morphisms (considering in the three cases a compactness condition). In particular, I will describe how the group cohomology controls deformations of these structures. This is a joint work with Ivan Struchiner (USP).

16:00-16:50

Speaker: Pablo Zadunaisky - IME-USP

Title: “TBA"
Abstract:

Friday, December 01

14:00-14:50
Speaker: Cristian Ortiz - IME-USP
Title: “Symplectic structures up to homotopy"
Abstract: In this talk we introduce the notion of symplectic structure up to homotopy. Examples will be discussed as well as the relation with shifted symplectic structures of Pantev-Toën-Vaquié-Vezzosi. We will also study Lagrangian morphisms in this setting and we will show a result which connects the notion of Lagrangian morphism with that of moment map in Dirac geometry.

15:00-15:50
Speaker: Carlos Gomes - IME-USP
Title: “Módulos de Gelfand-Tsetlin singulares para gl(n)"
Abstract: Na metade do século passado I. Gelfand e M. Tsetlin, descreveram bases explícitas para os gl(n)-módulos irredutíveis de dimensão finita e de peso máximo. Tais bases são parametrizadas pelas, desde então, chamadas tabelas de Gelfand-Tsetlin, cujos elementos (entradas) são números complexos que satisfazem certas condições envolvendo números inteiros. Observando que os coeficientes presentes nas fórmulas de Gelfand-Tsetlin (que descrevem explicitamente a ação dos elementos da base de gl(n) sobre essas tabelas) são funções racionais das entradas das tabelas, surgiu naturalmente a pergunta se não seria possível estender a construção feita por Gelfand-Tsetlin no referido trabalho para construir módulos mais gerais incluindo agora o caso dos módulos em que a dimensão fosse infinita. Essas ideias foram generalizadas por Y. Drozd, S. Ovsienko e V. Futorny, onde foram definidos os chamados gl(n)-módulos genéricos de Gelfand-Tsetlin (que são de dimensão infinita) e foram estabelecidas muitas propriedades rele- vantes desses módulos. Apoiando-se nessas ideias, V.Futorny, D. Grantcharov e L.E. Ramirez, definiram as tabelas 1-singulares de Gelfand-Tsetlin assim como o gl(n)-módulo cujos elementos são essas tabelas sujeitas a certas relações. Diz-se que uma tabela de Gelfand-Tsetlin é 1-singular se existe exatamente uma linha da tabela tal que nessa linha exista apenas um par de entradas $v_k_i$, $v_k_j$ tais que a diferença $v_k_i − v_k_j$ é um número inteiro. Além disso, diz-se que a tal tabela é genérica se tal par de entradas não existe ao longo de toda a tabela. Nessa palestra vamos apresentar algumas propriedades desses módulos assim como um critério (condição necessária e suficiente) para a irredutibilidade para tais módulos.

16:00-16:50

Speaker: Camilo Angulo - IME-USP
Title: “On a cohomology strategy for the integration of Lie 2-algebras"
Abstract: A Lie 2-algebra is a groupoid object in the category of Lie algebras. These can naturally be seen as an infinitesimal version of Lie 2-groups which are groupoids in the category of Lie groups. Lie 2-algebras are known to be integrable in this sense. In order to understand this integration process from a cohomological point of view, we present appropriate notions of representations for both Lie 2-groups and Lie 2-algebras, and the corresponding complexes whose cohomologies classify extensions. Finally, we discuss a van Est type theorem for a class of representations.