# Analysis and PDEs - Baptiste Devyver (Technion) - "Heat kernel estimates of Schrodinger-type operators"

Let us consider the heat equation:
$u_t+Lu=0$ in a domain $\Omega$.
Here, $L$ will be a self-adjoint Schrodinger-type operator of the form
abla^*
abla+R, acting on vector-valued functions $u(x,t)$ (or, more generally, on sections of a vector bundle over a Riemannian manifold), and $R$ is a potential term'' (often related to some curvature). We will present optimal estimates of the heat kernel under some smallness assumption on $R$. One of the main examples of application is estimating the heat kernel of the Hodge Laplacian $L=dd^*+d^*d$ acting on differential forms: in this case, we will be able to go beyond the traditional assumption of non-negativity of the curvature term, and to allow some amount of negative curvature.
Even in the particular case of scalar Schrodinger operators on a domain $\Omega$ of $\R^n$, our results are new.
This is a joint work with T. Coulhon and A. Sikora.

## Date:

Thu, 03/11/2016 - 13:00 to 14:00

Ross 70