Abstract: In this talk I will introduce the Langevin dynamics associated with Dyson Brownian motion and Dyson Brownian bridges. The main object is a singular system of SPDEs, the multilayer reflected stochastic heat equation (RSHE). It is the canonical infinite-dimensional Langevin dynamics whose invariant measures are laws of Dyson Brownian motion and Dyson Brownian bridges. The construction is motivated by Glauber dynamics for lozenge tilings. We show that, under a suitable scaling, the stationary Glauber dynamics converge to the multilayer RSHE. This is joint work with Pei-Ken Hung and Li-Cheng Tsai.