PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Mary Anne Raymond.

Title:The Gauss-Bonnet theorem via the heat equation.
Seminar:Slow Pitch Seminar
Speaker:Professor John Roe, Penn State University
Abstract:
Abstract: The Gauss-Bonnet theorem relates the Euler characteristic (vertices - edges + faces in any triangulation) of a closed surface with the "total curvature" of that surface. This classical result can be proved using Green's theorem. In this talk I'll explore an alternative proof, which is based on the short-term asymptotics of the equation that describes the flow of "vector-valued heat" on the surface. This method was developed by Patodi in the 1970s. It can be applied much more widely than just to the Gauss-Bonnet theorem and leads to many remarkable results relating geometry and analysis. But in this talk I'll try to avoid the temptation to generalize and focus attention on what is going on in the Gauss-Bonnet case.

Room Reservation Information

Room Number:MB106
Date:01 / 19 / 2010
Time:05:00pm - 06:10pm