Title: Strings, fermions and the topology of curves on surfaces
Speaker: Daniel Mathews (Monash University)
Abstract: Given a compact oriented surface with some marked points on its boundary, we construct a chain complex based on curves on the surface, with a differential defined by resolving crossings. This elementary construction, based on nothing more than the topology of curves on surfaces, turns out to have a rich and curiously "fermionic" algebraic structure, where differential modules and algebras, the Goldman bracket, string topology, and Weyl algebra representations all play a role. We will discuss how this construction in some cases is equivalent to, and in other cases appears to be a generalisation of, objects from sutured Floer homology, embedded contact homology, and categorical contact topology.