Seminar| Institute of Mathematical Sciences
Time: Thursday, September 17th, 2026,11:00-12:00
Location: IMS S408
Speaker: Ruoyuan Liu, University of Bonn
Abstract: In this series of lectures, we study the two-dimensional dispersive Anderson model (DAM), namely a nonlinear Schr\odinger equation with a multiplicative spatial white noise potential. The main strategy is based on the gauge-transform introduced by Hairer and Labb\'e (2015), which allows one to construct the solution as a limit of solutions to a family of regularized approximating equations.
We first discuss global well-posedness on the two-dimensional torus, emphasizing the construction and regularity of the relevant stochastic objects, as well as the role of modified energies and Strichartz estimates. We then consider the equation on the two-dimensional full space, where weighted Besov spaces become essential. If time permits, we will mention a large torus limit result for the two-dimensional DAM and the use of periodic weights.