Date/Time
Date(s) - 22/03/2024
1:30 pm - 2:30 pm

Date/Time: Friday March 22, 2024 (1:30-2:30pm)

Location: HH/410

Speaker: Michael Novack (Carnegie Mellon)

Title: Soap films, Plateau’s laws, and the Allen-Cahn equation

Abstract: Plateau’s problem of minimizing area among surfaces with a common boundary is the basic model for soap films and leads to the theory of minimal surfaces. In this talk we will discuss a modification of Plateau’s problem in which surfaces are replaced with regions of small but positive volume. The model captures features of real soap films that cannot be described by minimal surfaces. We will also discuss the PDE approximation of this problem via the Allen-Cahn equation and its relation to Plateau’s laws, which govern singularities in soap films.