In hopes of re-starting our seminar series, we will have our first virtual seminar via zoom on Monday, March 23 at 2pm. Before the seminar, we will begin with a virtual "town meeting" (again via zoom) from 1:30 to 2pm to just check with people on how everybody is doing during this uncertain period. Hope to see you there!
Zoom link: https://stanford.zoom.us/j/784962786
Despite being some of the first and most basic objects one encounters in the study of algebra, finite simple groups are surprisingly rich, and participate in a variety of mysterious connections to other areas in math and physics. The classification of finite simple groups is a remarkable theorem of pure mathematics which brings their mystique to bear. Indeed, much as in the more familiar classification of simple Lie groups, there are exceptional cases --- the so-called "sporadic groups" -- which are relatively poorly understood. Since group theory is the abstraction of the study of symmetry, it is natural to ask what structures exactly they act on by symmetries. Generalizing the observations of monstrous moonshine, we will argue that many of the sporadic groups naturally arise as the global symmetries of distinguished conformal field theories in two dimensions. In the process, we will be able to compute the torus partition functions of these theories by solving a kind of highly-constrained modular bootstrap problem using methods, old and new, from the theory of modular forms.