## Doctoral Thesis data

You may find my dissertation here:

**Title:**Amenability and coarse geometry of (inverse) semigroups and C*-algebras**Defense date:**March 5th, 2021**Grading:**excellent - cum laude

## Abstract

My dissertation studies some connections between different notions of amenability in C*-algebras, and connects these with algebraic and geometric conditions in inverse semigroups. Recall that an *inverse semigroup* is, roughly speaking, a set of partial bijections with commuting domains and ranges. One can approach these objects as one does with groups, and the thesis characterizes amenability in Day's sense as the existence of traces in some C*-algebra associated to the semigroup. Likewise, one can equip the semigroup with a right invariant metric, and study the property A of the resulting metric space. Doing so leads to numerous spaces, and we characterize when these have Yu's property A by means of the exactness of the reduced C*-algebra of the semigroup, generalizing a known characterization of Ozawa's. We also study numerous ramifications of these results with regards to groupoids, quasi-diagonality and the existence of amenable traces.