Talks

Umbral moonshine attaches mock modular forms and meromorphic Jacobi forms to automorphisms of the Niemeier lattices. It is now known that this association can be recovered from specific, graded modules for the Niemeier lattice automorphism groups. We will describe recent progress in a program to realize these modules explicitly.

It has become a platitute to say that black holes are fascinating objects—but they really are, in part because they challenge our understanding of the fundamental reversibility of physical processes.

In the first part of the talk, I will review some of the classical ways black holes behave as dissipative systems, such as the "hair loss” phenomenon and the monotonic growth of horizon area. In the second part, I will explain how quantum mechanics (more precisely, the coupling of black holes to the quantum vacuum) affects the classical picture at late times, notably through particle creation and evaporation. I will argue that techniques from two-dimensional field theory can help bring clarity to the associated “information loss”

problem, and perhaps also point to new, unexpected predictions. My approach will be as model-independent as possible; that is, rather than investigating a particular scenario for black hole evaporation, I will aim to derive generic consequences from basic assumptions regarding the reversibility of black hole evaporation.

We observe a relationship between the representation theory of the Thompson sporadic group and a weakly holomorphic modular form of weight one-half that appears in Zagier's work on traces of singular moduli and Borcherds products. We conjecture the existence of an infinite dimensional graded module for the Thompson group and use the observed relationship to propose a McKay-Thompson series for each conjugacy class of the Thompson group and then construct weakly holomorphic weight one-half forms at higher level that coincide with the proposed McKay-Thompson series. We also observe a discriminant property in this conjectured moonshine for the Thompson group that is closely related to the discriminant property conjectured to exist in Umbral Moonshine.