Speaker: Antoine Song (Caltech)
Title: Minimal surfaces, hyperbolic surfaces and random permutations
Abstract: Minimal surfaces and hyperbolic surfaces are both "optimal 2d geometries" which are ubiquitous in differential geometry. The first kind is defined by an extrinsic condition (the mean curvature vanishes), while the second kind is defined by an intrinsic condition (the Gaussian curvature is equal to -1). I will discuss a surprising connection between these two geometries coming from randomness. 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 is part of an attempt to bridge minimal surfaces and unitary representations. I will introduce this circle of ideas and mention some general questions.
URL associated with Seminar: https://web.math.osu.edu/colloquium/
