# Probability and Mathematical Physics Seminar

#### On microscopic derivation of a mean-curvature flow

**Speaker:**
Sunder Sethuraman, University of Arizona

**Location:**
Warren Weaver Hall 512

**Date:**
Friday, April 12, 2019, 11:35 a.m.

**Synopsis:**

We discuss a derivation of a continuum mean-curvature flow as a scaling limit of a class of particle systems, more robust than previous methods. We consider zero-range + Glauber interacting particle systems, where the zero-range part moves particles while preserving particle numbers, and the Glauber part allows creation and annihilation of particles. When the two parts are simultaneously seen in certain (different) time-scales, and the Glauber part is "bi-stable", a mean-curvature flow can be captured directly as a limit of the mass empirical density.

Such a "direct" limit might be compared with a "two-stage" approach: When the zero-range part is diffusively scaled but the Glauber part is not scaled, the hydrodynamic limit is a non-linear Allen-Cahn reaction-diffusion PDE. It is well-known in such PDEs, when the "bi-stable" reaction term is now scaled, that the limit of the solutions takes on stable values across an interface moving by a mean-curvature flow. This is joint work-in-progress with Tadahisa Funaki and Danielle Hilhorst.