Calendar

Feb
23
Fri
Colloquium: Rohit Nagpal (U. Chicago) @ Keller 401
Feb 23 @ 3:30 pm – 4:30 pm

Speaker: Rohit Nagpal
Title: Stability in the high dimensional cohomology of certain arithmetic groups

Abstract: Borel-Serre duality relates high dimensional cohomology of arithmetic groups to the low dimensional homology of these groups with coefficients in the Steinberg representation. We recall Bykovskii’s presentation for the Steinberg representation and explain its connection to modular symbols. Next, we describe the Steinberg representation as an object in a symmetric monoidal category, and use its presentation to describe an action of the free skew commutative algebra. Finally, we perform a Gröbner-theoretic analysis of this action to obtain new information on the homology of certain arithmetic groups with coefficients in the Steinberg representation. For example, we show that the sequence of homology groups H_1(Gamma_n(3), St_n) exhibit representation stability. This is an ongoing project with Jeremy Miller and Peter Patzt.

Mar
16
Fri
Talk Story with Thomas Hangelbroek
Mar 16 @ 3:30 pm – 4:30 pm
Mar
23
Fri
Colloquium: Christopher Marks (Cal. State Chico)
Mar 23 @ 3:30 pm – 4:30 pm
Apr
12
Thu
Undergraduate Seminar: Alex Schulte (Iowa State U.) @ Keller 402
Apr 12 @ 3:00 pm – 4:00 pm
Apr
17
Tue
Analysis Qualifying Exam
Apr 17 @ 9:00 am – 1:00 pm
Apr
24
Tue
Algebra Qualifying Exam
Apr 24 @ 9:00 am – 1:00 pm
May
22
Tue
Algebras and Lattices in Hawaii
May 22 – May 24 all-day
Mar
22
Fri
AMS Spring Central and Western Joint Sectional Meeting
Mar 22 – Mar 24 all-day