Overview
Advisor
Broadly, my interest is in the heat equation. More specifically, I study how the fundamental solution of the heat equation changes when the Laplacian in the equation is replaced by a Schrödinger operator. This situation produces connections between partial differential equations and Brownian motion, and may be studied in Euclidean space, on manifolds, or on fractals.
Research Focus
Heat kernel estimates, Schrödinger operators, Dirichlet forms
Publications
Pre-prints:
- Heat Kernel Estimates for Schrödinger Operators with Decay at Infinity on Parabolic Manifolds (joint with Laurent Saloff-Coste) https://arxiv.org/abs/2501.04221
- The Boundary Harnack Principle and the 3G Principle in Fractal-Type Spaces (joint with Laurent Saloff-Coste) https://arxiv.org/abs/2412.18671