DMS Analysis and Stochastic Analysis Seminar (SASA)

Speaker: Pierre Yves Gaudreau Lamarre (Syracuse University)

Title: Feynman-Kac formulas for Schrödinger operators with Matrix-white-noise

Abstract: In this talk, we will discuss recent progress toward proving new Feynman-Kac formulas for a class of Schrödinger operators perturbed by a matrix white noise. We will begin with a brief review of the classical Feynman-Kac formula from the point of view of applications in the spectral theory of "regular" Schrödinger operators. Then, we will introduce matrix white noise perturbations of Schrödinger operators, and briefly comment on the main source of motivation for studying such objects. Finally, we will discuss the main challenges that arise when attempting to extend the classical Feynman-Kac formula to matrix white noise perturbations.

Host: Le Chen