SPP 2026 - Subproject: Compactifications and local-global principles for Bruhat-Tits buildings

Basic data for this project

Description

We plan to study compactifications and local-global principles of Bruhat-Tits buildings. The compactifications will be constructed as horofunction completions, starting with asymmetric polyhedral norms on the maximal flats of the building. The ultimate goal is to study the dynamics of discrete group actions on the buildings. Our methods use ultraproducts, topolgical vector spaces and CAT(0) geometry.For the local-global principles we plan to study metric balls in the Chamber graphs of Bruhat-Tits buildings. Recent results for a special class of Bruhat-Tits buildings indicate that there is an interesting dichotomy between the case of function fields and p-adic fields, which we want to explore from a geometric viewpoint.