Parabolic geometries, BGG sequences and geometry at infinity

---

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.

---

Download ICS Download invitation