Zachary Porat : Cuspidal Cohomology for Iwahori Congruence Subgroups of $\mathrm{SL}(3, \mathbb{Z})$

Posted by Frederick Saia , part of the Number Theory Seminar.

At

March 13, 2026, noon

In

1227 SEO

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 $p$.  A natural question to ask is for what other congruence subgroups of $\mathrm{SL}(3, \mathbb{Z})$ can one perform analogous computations.  In this talk, we 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.  If time permits, we will discuss some improvements for the $\Gamma_0(3, p)$ setting as well. $$$$ Note the room change!