Geometry Seminar: P. Gaspar (U Chicago)

Geometry Seminar (Geometric Analysis)

Speaker: Pedro Gaspar (U Chicago)

Title: Phase transitions and mean curvature flows in the sphere

Abstract: The Allen-Cahn equation is a semilinear evolution PDE that models phase transition phenomena. Since the eighties, this equation has been used as a regularization for the mean curvature flow (MCF), providing a tool to construct and to study solutions of this geometric flow. In this talk, motivated by the connections between the stationary solutions for these problems, we will discuss the existence and asymptotics of eternal solutions to the Allen-Cahn equation on a round sphere, and how they can be used to construct a family of (weak) solutions to the MCF -- concretely, Brakke flows -- that connect minimal surfaces of low area.

This is joint work with Jingwen Chen (The University of Chicago).