Speaker: Geordie Williamson
Affiliation: University of Sydney
Abstract
In geometric representation theory cohomology, intersection cohomology and constructible sheaves show up everywhere. This might seem strange to an algebraic topologist, who might ask: why this emphasis on cohomology, when there are so many other interesting cohomology theories (like K-theory, elliptic cohomology, Brown-Peterson cohomology, complex cobordism, ...) out there? Also, is there something like "intersection K-theory", or "intersection complex cobordism"? This is something I've always wondered about. I will describe work in progress with Ben Elias, where we use Soergel bimodules to investigate what KU-modules look like on the affine Grassmannian. We have checked by hand that in types A1, A2 and B2, one gets something roughly resembling the quantum group. Speaking very roughly, the intersection K-theory of Schubert varieties in the affine Grassmannian should recover the irreducible representations of the quantum group.
About Pure mathematics seminars
We present regular seminars on a range of pure mathematics interests. Students, staff and visitors to UQ are welcome to attend, and to suggest speakers and topics.
Seminars are usually held on Tuesdays from 2 to 3pm.
Talks comprise 45 minutes of speaking time plus five minutes for questions and discussion.
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Researchers in all pure mathematics fields attend our seminars, so please aim your presentation at a general mathematical audience.
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To volunteer to talk or to suggest a speaker, email Ole Warnaar or Ramiro Lafuente.