Title: Lefschitz fixed point theorem for domains in C^n
Abstract: The Brouwer fixed-point theorem is a classical result stating that every continuous map from the closed unit ball to itself must have at least one fixed point. This admits a ubiquitous generalization for continuous self-maps on compact topological spaces in terms of the traces of the induced linear map on the singular cohomology spaces, known as the Lefschitz fixed point theorem. In this talk I will introduce and prove a Lefschitz fixed point formula of Donnely-Fefferman for suitable holomorphic automorphisms of a strictly pseudoconvex domain in $$C^n$$ in terms of the Bergman kernel associated to this domain. Time permitting, we also describe an application of this result to suitable circle actions on this convex domain.
