Abstract:

Minimal surfaces are surfaces which locally minimize the area, and they are ubiquitous in Differential Geometry. After giving a short and biased survey on constructions of minimal surfaces, I will discuss a recent paper connecting minimal surfaces in spheres and random matrix theory. The main statement is that there exists a sequence of closed minimal surfaces in Euclidean spheres, constructed from random permutations, which converges to the hyperbolic plane. This result came from an attempt to bridge minimal surfaces and unitary representations. I will try to describe this circle of ideas and some general questions.

Bio: 

Antoine Song is an assistant professor at Caltech. He obtained his PhD at Princeton with Fernando Codá Marques, before going to UC Berkeley for a postdoc.