Project Details
Projekt
A unified approach to Euclidean Buildings and symmetric spaces of non-compact type
Subject Area
Mathematics
Term
since 2020
Project identifier
Deutsche Forschungsgemeinschaft (DFG) - Project number 441721480
The present proposal concerns similarities between Euclidean buildings and symmetric spaces of non-compact type. The literature contains famous examples of theorems and properties which were first obtained in one case and then shown to hold true also in the other setting, for instance the existence of the spherical building at infinity. In this set-up one may also ask whether and which uniform statements and proofs can be obtained in both worlds. The main goal of this project is to show properties known from one world also in the other world, and to give uniform proofs of statements for both classes of spaces. In the former case, we would like to investigate the extendability of automorphisms of the visual boundary, and also filling properties of S-arithmetic groups. Regarding uniform Statements and results we aim to develop metric methods allowing for a simultaneous treatment of trees and rank-1 symmetric spaces, to uniformly establish the building-structure of the boundary at infinity, to investigate strongly transitive actions from a unified perspective, and to obtain a uniform proof of Kostant's convexity theorem.Mathematical methods to be used throughout the proposed research include CAT(0) geometry, group-theoretical, combinatorial and homological techniques as well as methods from coarse geometry and the combinatorics of folded galleries.
DFG Programme
Priority Programmes
Subproject of
SPP 2026:
Geometry at Infinity
