Graduate Student Seminar - Jeremy Gamble (Math)

Title: Spin structures and Dirac operators

Speaker: Jeremy Gamble

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.

As always, great food, coffee and drinks will be provided!

We hope to see you all this Friday! We encourage your participation in the seminar to provide continuity to this project.

You can visit the Grad Seminar website at https://uwomathgrad.github.io/editions/winter2020/