Geometry, Topology and Dynamics Seminar
Ben Lowe
University of Chicago
Minimal surfaces in negative curvature
Abstract: The geodesic flow of a compact negatively curved Riemannian manifold is one of the hallmark examples of a chaotic dynamical system, and there is a rich theory devoted to the interplay between the geometry of a negatively curved Riemannian manifold and the asymptotic behavior of its closed geodesics. Minimal surfaces are higher-dimensional versions of geodesics, that locally minimize area in the same way that geodesics locally minimize length. After giving an overview of the theory for geodesics, I will describe some recent work on the asymptotic behavior of minimal surfaces in negative curvature that is motivated by what is true for geodesics. Joint work with Andre Neves, and Yangyang Li and James Marshall Reber.
Wednesday April 15, 2026 at 3:00 PM in 636 SEO