Generic and Random Behavior of Minimal Surfaces

Explore the fascinating world of minimal surfaces in this 46-minute lecture by Antoine Song at BIMSA. Dive into the fundamental class of surfaces in Differential Geometry that locally minimize area. Gain insights into powerful variational methods for constructing minimal surfaces and understand their limitations in providing precise information on position and shape. Survey existing knowledge and discover two recent directions offering surprisingly quantitative information under "genericity" or "randomness" conditions. Learn about a collaborative study demonstrating the existence of a sequence of minimal surfaces that spatially equidistributes on average in generic closed Riemannian 3-manifolds. Examine how minimal surfaces in Euclidean spheres constructed from random permutations exhibit almost hyperbolic behavior with high probability in the large n limit.