Heat kernels for differential equation with potentials and applications
Der-Chen Chang
Georgetown University

Abstract:In this talk, we first introduce a geometric method based on multipliers to compute heat kernels for operators with potentials. Using the heat kernel, we may compute the fundamental solution for the Hermite operator with singularity at an arbitrary point on the Euclidean space and Heisenberg groups. As a consequence, one may obtain the fundamental solutions for the sub-Laplacian $\Box_J$ in a family of quadratic submanifolds.