EVENT DETAILS AND ABSTRACT

Title: The Behavior of the Heat Kernel at the Cut Locus
Speaker: Professor Robert Neel
Speaker Info: Columbia University
Brief Description:
Special Note:
Abstract:

It is well known that, on a compact Riemannian manifold, minus t times the logarithm of the heat kernel converges uniformly to the energy function as t goes to zero. Malliavin and Stroock have shown that this limit commutes with spatial derivatives away from the cut locus, but one expects more complicated behavior at the cut locus. In this talk we will give formulas for the small time asymptotics of the gradient and the Hessian of the logarithm of the heat kernel which are valid everywhere on the manifold and which admit a nice probabilistic interpretation. We will also show how these formulas can be used to study both the pointwise and the distributional limits of derivatives of the logarithm of the heat kernel.