Math Graduate Student Seminar

After recalling what the Dirac operator on Rn is, we will discuss how and when it's possible to extend that notion to a Riemannian manifold. To do so we'll need Clifford algebras and spinors, so we'll say what those are. We'll then square the Dirac operator and compare to the Laplace operator on spinors. This talk won't assume much background beyond knowing what a metric on a manifold is. (This is relevant background for the Index Theorem, noncommutative geometry, quantum field theory, Seiberg-Witten theory, and much more. If time permits we'll mention some of these applications.)