Inverse Problems for Minimal Surfaces

This talk explores a class of inverse problems where the goal is to determine the geometry of a minimal surface—and in some cases, the surrounding ambient space—from area data. These problems arise naturally in differential geometry and also appear in mathematical models inspired by theoretical physics, such as the AdS/CFT correspondence. We show how resolving such problems draws on a rich toolkit of methods, including nonlinear PDEs, integral geometry, and microlocal analysis. Time permitting, we conclude with a brief look at how recent machine learning techniques can be used to infer geometric structure from minimal surface data.