Topology Seminar

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

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.
Date: Monday, April 08, 2019
Time: 4:10pm
Where: Lunt 104
Contact Person: Eva Belmont
Contact email: ebelmont@northwestern.edu
Contact Phone: 847-467-1634
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