## Geometry Seminar - Abstracts

### Talk

Tuesday 1 October 2024, 16:00 - 17:00 in HG00.310

**Sophie Emma Zegers** (TU Delft)

*Classification of quantum lens spaces*

### Abstract

In the study of noncommutative geometry, various of classical
spaces have been given a quantum analogue. A class of examples are the
quantum lens spaces described by Hong and Szymański as graph \(C^*\)-algebras.
The graph \(C^*\)-algebraic description has made it possible to obtain important
information about their structure and to work on classification. Moreover,
every quantum lens space comes with a natural circle action, leading to an
equivariant isomorphisms problem.

In this talk, I will give an introduction on how to classify low
dimensional quantum lens spaces. We will also see how to obtain a number
theoretic invariant. Moreover, I will say a few words about a recent joint
work with Søren Eilers on the existence and construction of equivariant
isomorphisms of low dimensional quantum lens spaces.

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