Compactifications and Local-to-Global Structure for Bruhat-Tits Buildings

The project is concerned with rigidity, compactifications and local-to-global principles in CAT(0) geometry. One aim is to give a uniform construction of compactifications of euclidean buildings, using Gromov's embedding into spaces of continuous functions.

The ultimate goal is to study the dynamics of discrete group actions on the building, using the compactification.

The project also intends to investigate LG-rigidity and non-rigidity for the 1-skeletons and chamber graphs of general Bruhat-Tits buildings.

Bruhat Tits buidlings are simplicial analogs of symmetric spaces and are a fundamental tool to study algebraic groups over non-archimedian local fields. Their combinatorial structure encodes a lot of information about flag varieties and Grassmannians.