MATH Seminar

Title: Degeneration and the Determinant of the Laplacian
Seminar: Analysis and Differential Geometry
Speaker: David Sher of Stanford University
Contact: David Borthwick, davidb@mathcs.emory.edu
Date: 2012-01-24 at 4:00PM
Venue: MSC W301
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Abstract: When doing analysis on singular spaces, it is often useful to approximate them by smooth manifolds. In this spirit, we consider a family of smooth manifolds which degenerate to a manifold with a conical singularity, and analyze the behavior of various spectral-theoretic quantities under this degeneration. In particular, when we consider the behavior of the eigenvalues of the Laplacian and of the heat kernel, interesting structure becomes apparent. In this talk, I'll discuss this structure, and then discuss how it can be used to give an asymptotic expansion for the determinant of the Laplacian under conic degeneration. I'll also discuss applications and directions for further research.