Wednesday, February 26, 2020
Math Seminar Series
(Conferences / Seminars / Lectures)
Student Geometry/Topology more information...
Speaker: Keshav Sutrave
Title: A hot approach to the Hodge Theorem (Heat Equation)
Time: 4:10 PM - 5:00 PM
Place: C517 Wells Hall
The Hodge theorem is a result regarding Laplace's equation for differential forms on a Riemannian manifold (I will introduce the setup for this). Like many celebrated theorems in geometry, it gives a calculable geometric insight on the topology of the space. Normally, the method for solving this PDE is an "elliptic equation" procedure, but I will instead show a heat equation (parabolic) approach to the problem. We will see that the topology emerges in the long time behavior of the heat flow. Further work with this approach leads to results such as the Chern-Gauss-Bonnet theorem, and (almost literally) draws a line connecting geometry and topology.