The Regularized Determinant of a Four-Manifold

MEMBERS SEMINAR
Topic:The Regularized Determinant of a Four-Manifold
Speaker:Matt Gursky
Affiliation:University of Notre Dame and Member, School of Mathematics
Date:Monday, March 30
Time/Room:2:00pm - 3:00pm/S-101

I will give an overview of a variational problem in conformal geometry/spectral theory. Beginning with a formula for the determinant of the laplacian for a surface and the work of Osgood-Phillips-Sarnak, I will explain some attempts to generalize this work to four dimensions based on a formula of Branson-Orsted. The talk will be aimed at a general audience, and will be mostly a survey. Towards the end of the lecture I will briefly mention some work in progress, and indicate various technical issues that arise in 4-d that are absent in 2-d.