Date: Tuesday, November 18, 2014
Title: Revisiting classical results at the interface of number theory and representation theory
Abstract: The speaker will discuss recent work on Moonshine and the RogersRamanujan identities. The RogersRamanujan identities are two peculiar identities which express two infinite product modular forms as number theoretic qseries. These identities give rise to the RogersRamanujan continued fraction, whose values at CM points are algebraic integral units. In recent work with Griffin and Warnaar, the speaker has obtained a comprehensive framework of identities for infinite product modular forms in terms of HallLittlewood qseries. This work characterizes those integral units that arise from this theory. In a related direction, the speaker revisits the classical Moonshine Theorem which asserts that the coefficients of the modular jfunctions are dimensions of virtual characters for the Monster, the largest of the simple sporadic groups. There are 194 irreducible representations of the Monster, and it has been a longstanding open problem to determine the distribution of these representations in Moonshine. In joint work with Griffin and Duncan, the speaker has obtained exact formulas for these distributions.
Speaker: Ken Ono
Institution: Emory University
