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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
Lab building west seminar room

Abstract:

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.
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