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

• Applicants: Professor Dr. Linus Kramer; Professorin Dr. Petra Nora Schwer
• Subject Area: Mathematics
• Term: from 2017 to 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 336349957

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.

• DFG Programme: Priority Programmes
• Subproject of: SPP 2026: Geometry at Infinity
• International Connection: Belgium, Switzerland, USA
• Cooperation Partners: Dr. Corina Ciobotaru; Professor Dr. Hendrik van Maldeghem; Professor Dr. Richard M. Weiss