Title: Geometric compactifications and parabolic geometries

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.