Parabolic geometries, BGG sequences and geometry at infinity
Date:
Thursday, March 29, 2018 13:00 - 15:00
Speaker:
Andreas Cap (University of Vienna)
Location:
Big Seminar room Ground floor / Office Bldg West (I21.EG.101)
Series:
Mathematics and CS Seminar
Host:
Tamas Hausel
Contact:
DE ANTONI Jessica
Generalized flag varieties are homogeneous spaces of the form G/P, where G is a semisimple Lie group and P is a parabolic subgroup of G. If G is a complex semisimple group, these are exactly the compact homogeneous spaces of G and they are known as rational homogeneous varieties. I will start by exhibiting a geometric content in the action of G on G/P, thus leading to the idea of parabolic geometries. Next, I will discuss BGG (Bernstein-Gelfand-Gelfand) sequences based on a refinement of twisted de Rham complexes over G/P. In the second part of the talk, I will outline how this theory can be applied to the study of geometric compactifications and how it leads to several generalizations of the concept of conformally compact manifolds.