Geometric Analysis and Topology Seminar

---

Harmonic map methods in spectral geometry and applications to minimal surfaces

Speaker: Daniel Stern, University of Chicago

Location: Online

Videoconference link: https://nyu.zoom.us/j/94747124588

Date: Wednesday, May 11, 2022, 11 a.m.

Synopsis:

About fifty years ago, Joseph Hersch observed that the round metric on the 2-sphere maximizes the first (nonzero) eigenvalue of the Laplacian among all metrics of the same area. In the decades since, the study of metrics maximizing Laplace eigenvalues on surfaces has led to a number of striking developments, revealing in particular some deep and surprising connections to harmonic maps and minimal surfaces in spheres. In this talk, I'll describe recent results relating these problems to natural variational constructions for harmonic maps, and discuss applications to the study of maximizing metrics for Laplace and Steklov eigenvalues, and the associated minimal surfaces. (Joint with Mikhail Karpukhin.)