Maseeh Mathematics + Statistics Colloquium Series Presents: Modular functions and the monstrous exponents

Speaker: Dr. Holly Swisher, Oregon State University

Title: Modular functions and the monstrous exponents

Abstract: In 1973 Ogg initiated the study of monstrous moonshine with the observation that the prime divisors of the monster group are exactly those for which the Fricke quotient X0(p)+p of the modular curve X0(p) has genus zero. Here, motivated by Deligne's theorem on the p-adic rigidity of the elliptic modular j-invariant, we present a modular function-based approach to explaining some of the exponents that appear in the prime decomposition of the order of the monster.

Biography: Professor Swisher received her Ph.D. in Mathematics from the University of Wisconsin - Madison in 2005, under the supervision of Professor Ken Ono. She was a Ross Assistant Professor in the Department of Mathematics at the Ohio State University from 2005-2006 before joining the Mathematics Department at Oregon State in 2006. Professor Swisher is a researcher in the areas of number theory and combinatorics. Her current work is focused on modular forms, partition theory, and hypergeometric series, including the interplay between them.