### Inverse semigroups as metric spaces, and their uniform Roe algebras

Geometry and Topology Seminar

2nd May 2023, 2:00 pm – 3:00 pm

Fry Building, 2.04

Since Gromov's work in the 90s, studying groups as metric spaces has become a main trend in group theory. It turns out that there is a strong link between some of the algebraic properties of the group and some of the large scale geometric properties of the metric associated to it, and in some cases, this links to properties of a C*-algebra called the uniform Roe algebra associated to the metric space. In the past few years, some of these results have been extended to so-called inverse semigroups by Chung, Gray, Martínez, Lledo, Silva, and the speaker. Inverse semigroups are a generalization of groups which encapsulate partial symmetries similarly as to how groups encapsulate symmetries. During the talk, we will give an introductory exposition of these results.

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