Presented by: 
Prof. Xianzhe Dai, University of California, Santa Barbara, USA
Tue 18 Apr, 2:00 pm - 3:00 pm

Abstract: By conical degeneration we mean a family of smooth Riemannian manifolds degenerating into a singular Riemannian manifold with singularity of conical type. This type of singular limit appears quite often.
We look at the special case when a K3 surface degenerates into an orbifold and study the limiting behavior of certain geometric invariants defined in terms of the heat kernels. As an application we find remarkable connection between these geometric invariants and certain modular forms of Borcherds. This is joint work with Ken-Ichi Yoshikawa.