Differential Geometry Seminars 2022

Boundary behaviour of nonlocal minimal surfaces

Surfaces which minimize a nonlocal perimeter functional exhibit quite different behaviors from the ones minimizing the classical perimeter. We will investigate some structural properties of nonlocal minimal surfaces, and in particular we will discuss the "stickiness phenomenon", namely the strong tendency of adhering at the boundary of the reference domain.

Wess-Zumino-Witten models: integer versus fractional levels

The nonnegative-integer-level Wess-Zumino-Witten models are well known toy models for strings propagating on curved spacetimes. They have beautiful mathematical properties, for example the modules of the associated vertex operator algebra form a modular tensor category.

Less well known are their fractional-level cousins. Interest in these has surged recently because of applications to the 4D/2D correspondence of Beem et al, new approaches to affine W-algebras related to the geometric Langlands program, and ongoing interest in logarithmic conformal field theory.

I will review some of what is known about the integer and fractional cases in the simplest example. If time permits, I will discuss a new technique for fractional cases to classify modules and understand their modularity

The Riemann Hypothesis: severely undervalued at a meagre one million dollars

Even though a solution to the Riemann Hypothesis lands the luck solver with a million dollars (and USD at that!) this still seems very cheap, given the difficulty of the problem. I shall outline some history of the problem and the very limited partial progress towards it.