EVENT DETAILS AND ABSTRACT

Title: High dimensional cohomology of congruence subgroups
Speaker: Jeremy Miller
Speaker Info: Purdue University
Brief Description:
Special Note:
Abstract:

The level p congruence subgroup of SL_n(Z) is defined to be the subgroup of matrices congruent to the identity matrix mod p. These groups have finite cohomological dimension. In the 1970s, Lee and Szczarba gave a conjectural description of the top dimensional cohomology groups of these congruence subgroups. In joint work in progress with Patzt and Putman, we show that this conjecture is false for p>5. In particular, these congruence subgroups have extra cohomology classes in their top degree cohomology coming from the first homology group of the associated compactified modular curve. I will also discuss joint work with Patzt and Nagpal on a stability pattern in the high dimensional cohomology of congruence subgroups.