Title: Geometric compactifications and parabolic
Abstract: The talk discusses applications of the
theory of parabolic
geometries to the study of geometric
compactifications. The focus is
on the simplest examples of conformal
and projective structures.
Parabolic geometries admit a uniform
description as Cartan geometries
and it turns out that holonomy
reductions of Cartan connections provide
a conceptual approach to a variety of
different types ofcompactifications.
I will discuss the example of
conformally compact metrics, including
Poincare-Einstein metrics, as well as
an analogous concept that builds on
projective differential geometry from
this perspective. Also, applications
to compactifications of symmetric
spaces will be discussed briefly.