Talk by Jeremy Gamble (Math Colloquium)

Title: Spin structures and Dirac operators 

Abstract: Spin structures and Dirac operators play an important role in many areas of mathematics, such as mathematical physics, index theory and differential geometry. The Dirac operator is like a "square root" of the Laplacian, and can always be defined on a manifold which has a spin structure.

In the talk, I will introduce Clifford algebras, Spin and some elements from differential geometry in order to define spin structures and Dirac operators. I will motivate these objects with some examples from physics, and present some theorems such as an obstruction for the existence of a spin structure, some basic properties of Dirac operators. 

Some familiarity with differential geometry will be assumed.

https://uwomathgrad.github.io/editions/winter2020/