Coarse geometry and C*-algebras

This PhD project is in pure mathematics, more specifically somewhere between metric geometry, geometric group theory and functional analysis.

To explain the idea of coarse geometry, one may imagine looking at a metric space from further and further distance, until all the local phenomena are washed out. The features that remain visible are the ones that are studied by coarse geometry. This perspective, pioneered by J. Roe on the analytic side and M. Gromov on the group theory side, has been immensely successful in various branches of pure mathematics.

Many applications of coarse geometry (e.g. the Novikov conjecture, the coarse Baum-Connes conjecture, index theorems, positive scalar curvature problems) use functional analytic technology on the way, namely C*-algebras and K-theory.

This research area is quite wide, so the actual focus of the PhD project is flexible: either more coarse geometric in nature (in which case a functional analytic background is not required, but welcome), or more C*-algebraic (in which case a functional analytic background is an advantage). This project will provide a grounding in modern functional analysis and geometric group theory at the cutting edge of research.

Possible concrete problems include studying coarse median structures (connected with geometric group theory), and studying connections between asymptotic dimension, dynamical notions of a dimension (group actions) and nuclear dimension of C*-algebras (classification of C*-algebras).