Cuspidal Cohomology Computations for Congruence Subgroups of $\mathrm{SL}(3, \mathbb{Z})$

Abstract: Ash, Grayson, and Green computed the action of Hecke operators on the cuspidal cohomology of congruence subgroups $\Gamma_0(3, p) \subseteq \mathrm{SL}(3, \mathbb{Z})$ for small $p$. The first part of the talk will discuss how we extended their work, gathering additional data for larger $p$ using a new technique which allows for computations directly on the space of interest. A natural question to ask is for what other congruence subgroups of $\mathrm{SL}(3, \mathbb{Z})$ can one perform analogous computations. In the second part of the talk, we will detail techniques for working with congruence subgroups that are Iwahori at $p$, providing a framework for understanding the action of Hecke operators on the corresponding cohomology.

number theory

Audience: researchers in the topic

( paper )

Five College Number Theory Seminar