Hora: 13:10h
Local: B106b

Terça 21 de Março:
Título: “Conjectura de Kepler”
Palestrante: Víctor Vergara.

Quinta 23 de Março:
Título: “Folheações complexas com estrutura transversalmente afins em codimensão arbitrária”
Palestrante: Liliana Jurado

Data: 22/03/2017 (quarta-feira)
Hora: 13:30h
Local: C116

Palestrante: Pedram Hekmati (IMPA)

Título: String structures and Courant algebroids 

Resumo: A string structure is a higher analogue of a spin structure on manifolds. Its existence is obstructed by the first Pontryagin class, which itself is tied to a certain class of transitive Courant algebroids. In this talk, I will review these two notions and explain how they are linked by a reduction procedure introduced by Bursztyn-Cavalcanti-Gualtieri. Time permitting, I will explain how to do geometry and implement T-duality on these transitive Courant algebroids.

Data: 15/03/2017
Hora: 15:05h
Local: C116

Palestrante: Roberto Rubio (IMPA)

Título: Higher analogues of symplectic, Poisson and Dirac structures 

Resumo: We will first review how symplectic and Poisson structures on a manifold M fit into Dirac structures (integrable Lagrangian subbundles of TM+T*M), and then introduce higher versions of symplectic and Poisson structures. Having a higher version of Dirac structures is more troublesome than expected. Indeed, whereas the graph of a Poisson structure is a Dirac structure, and hence Lagrangian, the graph of a higher-Poisson structure, lying on TM plus the k-th exterior power of T*M, is not necessarily Lagrangian. To fix this, we introduce the notion of a weak-Lagrangian subspace and define higher-Dirac structures as integrable weak-Lagrangian subbundles, so that higher-Poisson structures do correspond to higher-Dirac structures transversal to TM. Higher-Dirac structures are, in particular, Lie algebroids, so their projection to TM is an involutive distribution and hence induces a (singular) foliation on M. A precise linear algebraic description of weak-Lagrangian subspaces allows us to describe the geometry appearing on the induced foliation, which is a non-trivial higher version of the presymplectic foliation of a Dirac structure. This is joint work with H. Bursztyn and N. Martínez-Alba.