Discrete isometry groups of the infinite-dimensional hyperbolic space and convex-cocompact representations

Date
2025/07/29 Tue 15:00 - 16:00
Room
6号館609号室
Speaker
David Xu
Affiliation
Korea Institute for Advanced Study
Abstract

Similarly to Euclidean spaces, there is an infinite-dimensional analog for the (algebraic) hyperbolic spaces. This space enjoys all the "geometric" properties of its finite-dimensional siblings. However, the topological aspects of this space and its group of isometries are more involved than in finite dimension. In particular, even the notion of discrete isometry groups needs to be specified in this context. In this talk, I will present the infinite-dimensional hyperbolic space and describe some of its properties, emphasizing some differences with finite dimensions. Then, I will discuss some ways of finding "discrete" subgroups of isometries by bending convex-cocompact representations of surface groups arising from the exotic representations of Monod and Py.