Time: 10:05am
Speaker: Ranit Bose
Title: The Geometry of Donaldson-Witten theory

Abstract: Edward Witten famously formulated the Donaldson invariants of smooth four-manifolds as correlation functions of certain operators in a supersymmetric topological quantum field theory (TQFT), called Donaldson-Witten theory. My thesis is primarily concerned with a differential geometric interpretation of the Lagrangian of the theory. In this talk, I will discuss the main ideas used to arrive at the Lagrangian through purely geometric considerations. This includes generalisations of the Chern-Gauss-Bonnet theorem, related theorems arising from Poincare duality, and finally how we can formally apply it to the infinite dimensional context of Donaldson invariants.  

Time: 10:40am
Speaker: Georgiana Lyall
Title: The pure planar braid group

Abstract: The planar braid group is a 2-dimensional analogue to the more commonly known braid group. It has a finite index subgroup called the pure planar braid group. There is a straightforward presentation for the planar braid group, but it is much harder to describe the pure subgroup. In this talk we will introduce these groups, and then show how geometric methods can be used to help us understand this subgroup.