## Geometry, Topology and Dynamics Seminar

Marco Guaraco

University of Chicago

Geometric Aspects of the Allen-Cahn Equation on closed manifolds

**Abstract:**In this talk I will discuss both local and global properties of the stationary Allen-Cahn equation in closed manifolds. This equation arising from the theory of phase transitions has a strong connection with the theory of minimal hypersurfaces. I will summarize recent results regarding the analogy between both theories focusing on min-max constructions. Among other things, I will explain how the analogy provides a new PDE-based proof of Almgren-Pitts theorem about the existence of a minimal hypersurface in any closed manifold.

Monday February 19, 2018 at 3:00 PM in SEO 636