Title: Moments of the two-dimensional stochastic heat equation.
Abstract: The stochastic heat equation (driven space-time white noise) arises from interface growth dynamics via the Kardar-Parisi-Zhang equation and from the theory of disordered systems via continuum directed random polymers. Despite these physical relations, many fundamental questions for the stochastic heat equation above one dimension remain open. In particular, two dimensions are the critical dimensions for the stochastic heat equation and are known for much more subtle properties.
In this talk, I will begin with an overview of the stochastic heat equation. Then I will turn to the setting of two dimensions and explain connections between (1) the moments of certain solutions from renormalizing the noise and (2) a solvable quantum mechanical system given by the many-body Bose gas with delta-function potentials. Accordingly, the last part of the talk will concentrate on related constructions of the Bose gas dynamics, with an emphasis on a Euclidean, probabilistic analytic view.
Zoom link for remote access: https://mcgill.zoom.us/j/89866454424?pwd=OGxsVTRheUtzRU9uV2JVN0VOUi8vZz09