Speaker: Chen-Kuan Lee
University of Notre Dame
Will give a Graduate Student Geometry Seminar entitled:
The Space of Minimal Submanifolds for Varying Riemannian Metric
Abstract: Let $N$ be a smooth manifold and let $\mathcal{M}$ be the space of pairs $(\gamma, M)$ where $\gamma$ is a smooth Riemannian metric on $N$ and $M \subset N$ is a minimal submanifold with respect to $\gamma$. In 1990, Brian White showed that $\mathcal{M}$ is a Banach manifold and that the projection $\Pi: (\gamma, M) \rightarrow \gamma$ is a smooth map of Fredholm index 0. Together with Lawson's conjecture, which was proved by Simon Brendle in 2012, it follows that every metric of positive Ricci curvature on $\mathbb{S}^3$ admits a minimal embedded torus.
Date: 10-18-2024
Time: 4:00 pm
Location: 258 Hurley Bldg