### Thursday, March 24, 2016 (10:00 a.m. in Yost 306)

**Title: **Rademacher Sums, Hecke Operators, and Moonshine

**Student:** Paul Bruno

**Advisor:** John Duncan (Assistant Professor, Emory University)

**Committee Members:** David Singer, Elisabeth Werner, and Colin McLarty (Philosophy)

**Abstract: **In this talk, we analyze the actions of Hecke operators on Rademacher sums. To investigate the problem, we consider the coefficients of the Fourier expansion of a Rademacher sum. We derive explicit formulae for these coefficients and prove a number of relationships between them. Using this analysis, we identify distinguished families of Hecke operators for a large class of discrete groups of isometries of the hyperbolic plane.