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.