Samuel Eilenberg Lectures

Speaker: Simon Brendle (Stanford University)

Title: “Partial Differential Equations in Geometry”

Abstract: “A central theme in geometry is the study of manifolds and their curvature. In this lecture series, we will discuss how techniques involving partial differential equations have shed light on several longstanding problems in global differential geometry. In the first part of the course, we will focus on the geometry of hypersurfaces, and discuss our proof of Lawson’s conjecture concerning minimal tori in S^3, as well as new results on mean curvature flow with surgery. In the second part, we will focus on the Ricci flow, including the Differentiable Sphere Theorem and Perelman’s question concerning the uniqueness of the Bryant soliton.”