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High-dimensional cohomology of special linear and symplectic groups

Ponente: Benjamin Brück
Institución: ETH Zürich
Tipo de Evento: Investigación
Cuándo 25/11/2021
de 13:00 a 14:00
Dónde En linea (zoom)
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Computing the cohomology of arithmetic groups is a fundamental and often difficult problem at the intersection of topology, group theory and number theory. In this talk, I will explain how one can use duality phenoma to compute the rational cohomology of the arithmetic groups SLn(Z) and Sp2n(Z) in "high" dimensions, i.e. close to their virtual cohomological dimension. Specifically, I will talk about joint work with Miller-Patzt-Sroka-Wilson in which we show that Hn(n-1)/2 - 2(SLn(Z); Q) = 0 for n>3. This was previously unknown, but confirms a conjecture of Church-Farb-Putman. In ongoing work with Patzt-Sroka, we are also trying to adapt these techniques to the group Sp2n(Z).