Speaker: Rufus Willett

Title: Positive curvature and index theory.

Abstract: Starting with two-dimensional surfaces, I’ll introduce positive (scalar) curvature. I’ll then discuss the relationship of this to index theory, a theory that counts the number of solutions to certain partial differential equations. Finally, I’ll mention the relevance of K-theory, a way of generalizing the notion of dimension of a vector space from fields to arbitrary rings.