Title: Recent results in the study of groups of moonshine-type
Speaker: Jay Jorgenson (CCNY)
Abstract: We will present results obtained in studying the spectral theory and holomorphic function theorem associated to the groups denote by $\Gamma_{0}(N)^{+}$, which are obtained by "adding" the Fricke involutions to the principal congruence groups. If $N$ is square-free and the associated quotient space has genus zero, then the groups arise in the theory of "monstrous moonshine". In addition to theoretical considerations, we employed extensive computer programs in order to, for example, determine canonical generators of the function fields for all genus one, two and three groups. The work is joint investigations with Lejla Smajlovic and Holger Then.
Seminar URL: https://research.math.osu.edu/numbertheory/