Coarse Geometry and Inverse Semigroups

Document Type

Presentation Abstract

Presentation Date

11-25-2019

Abstract

In this talk we will discuss, mainly, two seemingly disconnected notions in mathematics: coarse geometry and inverse semigroups.

Geometry often studies certain objects (such as sets or manifolds) equipped with a distance function. For instance, one classical problem would be to classify every compact manifold up to diffeomorphism. Coarse geometry shifts the point of view, and defines two sets to be coarse equivalent if they look the same from far away. In this way, for instance, a point and a sphere are indistinguishable from each other. Coarse geometry then studies properties that remain invariant under this weak equivalence relation, that is, properties of the space that only appear at infinity.

On the other hand, an inverse semigroup is a natural generalization of the notion of group, and is closely related to the idea of groupoid. Starting with one of these objects we will introduce how to construct a metric space, in the same fashion as the Cayley graph construction in the context of groups. We will then study its coarse structure, in particular its property A and its amenability. Time permitting, we will also relate these properties to analogue properties in some operator algebras.

Additional Details

Monday, November 25, 2019 at 3:00 p.m. in Math 103
Refreshments at 4:00 p.m. in Math Lounge 109

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