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Research project

Boundary representations of non-positively curved groups

Project overview

This project fits into the framework of Noncommutative Geometry, in particular research related to the Baum--Connes conjecture, analysis on groups, and representation theory. The Baum--Connes conjecture connects geometry, topology and algebra. From one point of view, it proposes a way to understand the algebraic topology (K-theory) of (a part of) the representation space of a group. While it is possible to effectively describe all the representations of (semisimple) Lie groups, this task is impossible for discrete groups in general.

We propose to construct explicit families of representations for large classes of discrete groups, using geometry (non-positive curvature) and boundaries. They directly address important questions (Shalom's conjecture), relate to existing approaches to the Baum--Connes conjecture, and harmonic analysis on discrete groups. The proposed pathway combines ideas from analytic and geometric group theory, representation theory of Lie groups and random walks.


Lead researcher

Dr Jan Spakula

Associate Professor

Research interests

  • C*-algebras, noncommutative geometry
  • geometric and analytic group theory
  • coarse geometry

Collaborating research institutes, centres and groups

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