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University of Sydney Algebra Seminar

Eran Assaf

Friday 7 February, 12-1pm, in the SMRI Seminar room (McLeay Building A12, Room 301)

Structure in the cohomology of arithmetic groups

I will discuss ongoing work seeking to understand the cohomology of various arithmetic groups (equivalently the top weight cohomology of various Shimura varieties). The key idea is that this piece of cohomology is encoded combinatorially via the boundary complex of a compactification of the Shimura variety, which is shown to have a structure of a Hopf algebra. This is ongoing joint work with Madeline Brandt, Juliette Bruce, Melody Chan, and Raluca Vlad.