Department of Mathematics - UC Santa Barbara

Geometry, Topology, and Physics Seminar, Winter 2010

Organizers: Andreas Malmendier and Dave Morrison.
Meets 4:00 - 5:30 p.m. Fridays in South Hall 6635.

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Feb. 12

The seminar will meet at 3:00pm in SH 6617.

Boris Vertman (Stanford University)

Heat Kernel and Analytic Torsion on Manifolds with Edge Singularities.

This talk will be a part of the Differential Geometry Seminar.

Abstract: We discuss the construction of the heat kernel for the Friedrichs extension of the Hodge Laplacian on Riemannian manifolds with non-iterated incomplete edge singularities. We derive the heat trace asymptotics and define the analytic torsion in this singular setup. We discuss variation of the analytic torsion under metric changes. Under additional conditions on the dimension and metric structures the analytic torsion is shown to form a topological invariant, independent of the particular choice of an edge metric.