# Analysis Seminar

#### Homogenization of (parabolic) geometric flows in periodic media - recent developments

**Speaker:**
Peter Morfe, Max Planck Institute, Leipzig

**Location:**
Warren Weaver Hall 1302

**Date:**
Thursday, May 11, 2023, 11 a.m.

**Synopsis:**

I will discuss recent work on the homogenization of geometric flows in periodic media in the parabolic scaling regime, with particular focus on the Allen-Cahn equation with periodic coefficients. Classically, the scaling limit of the Allen-Cahn equation is mean curvature flow. So far, generalizing this fact to the periodic setting remains elusive. I will explain some recent work in this direction, which elucidates some of the obstructions and also yields some partial (positive) results. The main takeaway will be that this problem brings together difficulties from at least three different areas: Aubry Mather theory; the homogenization of gradient flows; and statistical physics.