Discrete Algorithms for Geometric Topology

Jonathan Spreer (Sydney)

Abstract

Geometric topology is a field of research in which many fundamental problems turn out to be algorithmically solvable. This fact makes the field an application area for discrete algorithms.

In this talk I will sketch how (standard) knowledge on discrete algorithms helps advance the study of manifolds (surfaces and their higher-dimensional analogues -- the protagonists in geometric topology) and, conversely, how this research can produce results which may be of interest for other more applied fields such as computational geometry and (parameterised) problem complexity.