April 16, 2025
This lecture series is scheduled to take place on Monday, May 12, Thursday, May 15, and Friday, May 16.
How Curved are Level Sets of Solutions to Elliptic PDE?
We will discuss a new geometry of level sets of semilinear elliptic equations, \( \Delta u = f(u) \), inspired by the work of Hamilton and Perelman on mean curvature flow and Ricci flow. There are potential applications to levels sets of eigenfunctions, but we are just getting started with harmonic functions. In doing so, we will describe two of the most basic tools of algebraic and differential geometry, Jacobi functions and the affine connection of Levi-Civita.