Discrete Morse Theory for the pure mathematician

Abstract

Discrete Morse Theory was introduced by Forman as a tool to find simpler homotopy equivalent versions of given CW complexes. This is extensively used in applied areas of maths such as Topological Data Analysis, but it has recently found some applications in pure maths, thanks to a homological algebra version due to Sköldberg. In this talk I will give an introduction to DMT and describe some of these applications, for instance, in the study of categorified braid groups.