# Klas Erninger: Algebraic simplifications of metric information

Master Thesis Presentation

**Time: **
Tue 2020-06-30 13.00 - 14.00

**Location: **
Zoom, email organiser

**Lecturer: **
Klas Erninger

### Abstract

This thesis is about how to interpret metric data with topological tools, such as homology. We show how to go from a metric space to a topological space via Vietoris-Rips complexes. We use the usual approach to Topological Data Analysis (TDA), and transform our metric space into tame parametrised vector spaces. It is then shown how to simplify tame parametrised vector spaces. We also present another approach to TDA, where we transform our metric space into a filtrated tame parametrised chain complex. We then show how to simplify chain complexes over fields in order to simplify tame parametrised filtrated chain complexes.

**Zoom Note:** Please email
wojtek@kth.se
if you are interested in getting the meeting-ID.