Speaker: Renmin Song, University of Illinois, Urbana-Champaign.

Title: Heat kernel estimates for (fractional) Laplacians with supercritical killings.

Abstract:

In this talk, I will present some recent results on sharp two-sided estimates on  the heat kernels of ( fractional) Laplacians with supercritical killing potentials, that is, heat kernels of operators of the form
$$
-(-\Delta)^{\alpha/2}-\kappa (x)
$$
where $\alpha\in (0, 2]$ and $\kappa$ belongs to a class of positive supercritical potentials including $\kappa(x)=c|x|^{-\beta}$ with $\beta>\alpha$. This talk is based on a joint paper with Soobin Cho, and a joint paper  with Soobin Cho and Panki Kim.

This talk is aimed at a general audience and I will start with some basic materials.