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Complex Analysis, Dynamics and Geometry Seminar

[TOPOLOGY SEMINAR] Computing high-dimensional group cohomology via duality
Monday, October 3, 2022
4:00-5:00 PM
3096 East Hall Map
In recent years, duality approaches have yielded new results about the high-dimensional cohomology of several groups and moduli spaces, such as SL_n(Z) and M_g. I will explain the general strategy of these approaches and survey results that have been obtained so far. To give an example, I will first explain how Borel-Serre duality can be used to show that the cohomology of SL_n(Z) vanishes near its virtual cohomological dimension. This is based on joint work with Miller-Patzt-Sroka-Wilson and builds on results by Church-Farb-Putman. I will then put this into a more general context by giving an overview of analogous results for mapping class groups of surfaces, automorphism groups of free groups and further arithmetic groups such as SL_n(O_K) and Sp_{2n}(Z). Speaker(s): Benjamin Brück (ETH Zürich)
Building: East Hall
Event Type: Workshop / Seminar
Tags: Mathematics
Source: Happening @ Michigan from Department of Mathematics