Palestrante: Lázaro Rodríguez (Unicamp)
Título: G_2 holonomy manifolds are superconformal.
Resumo: Given a manifold with G_2 holonomy we prove the space of global sections of the chiral de Rham complex contains two commuting copies of the Shatashvili-Vafa superconformal algebra. This algebra appears as the chiral algebra associated to the sigma model with target a G_2 holonomy manifold. I will discuss how the structure and representation theory of this vertex algebra can be used to unravel the geometry and topology of the underlying manifold.
Palestrante: Olivier Glorieux (IMPA)
Título: Critical exponent for globally hyperbolic, anti-de Sitter
Resumo: Critical exponent is a dynamical invariant measuring the exponential growth rate of number of closed geodesics. It has been extensively studied for hyperbolic manifolds. Anti-de Sitter manifolds are Lorentzian manifolds of constant curvature $-1$, it is the Lorentzian counterpart of the hyperbolic space. A subclass of Lorentzian manifolds, called globally hyperbolic, have nice properties making them look like quasi-Fuchsian hyperbolic manifolds. For globally hyperbolic, anti-de Sitter manifolds, we will explain how to define a notion of critical exponent and how it is related, as in the hyperbolic case, to the Hausdorff dimension of the limit set. We will not suppose any backgrounds
on Lorentzian geometry and recall all the basic definitions. Our aim is to explain similarities and differences between Anti-de Sitter geometry and hyperbolic geometry, from a dynamical point of view.
Palestrante: Pedro Frejlich (PUC-Rio)
Título: Homotopy Invariance in Lie Theory
Resumo: In this talk, we approach the notion of homotopy invariance in the real of Lie theory via deformation of transversals. This perspective unifies several seemingly unrelated phenomena, and offers new insight into the pullback construction. Part of joint work with I. Marcut, U. Radboud (Nijmegen).