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Representation theory without vector spaces

Julia Pevtsova
Thursday, February 15, 2024 - 4:30pm to 5:30pm
PDL C-038

Classically, representation theory studies symmetries encoded as actions of group-like objects on vector spaces. A celebrated theorem of Deligne from 2002 explained that abstract categorical symmetries in characteristic zero are still governed by classical ``supersymmetries” and have super vector spaces lurking in the background. In positive characteristic the situation is much wilder: we don’t yet have a good understanding of what it is that is lurking. It is definite, though, that there is a lot there beyond vector and super vector spaces. I will try to describe where the new theory meets the old and what we do (not much) and don’t (a lot) know.

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