Emily Cliff (University of Urbana-Champaign)

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Emily Cliff (University of Urbana-Champaign)

February 24, 2017 @ 2:00 pm - 3:00 pm UTC+0

Universal O-modules and representations of the automorphism group of a formal disk

Universal O- and D-modules (introduced by Beilinson and Drinfeld) arise in the study of the equivalence between certain categories of vertex algebras and chiral algebras. A universal O-module of dimension d is an assignment of a quasi-coherent sheaf to each smooth variety of dimension d, in a way compatible with ├ętale morphisms between the varieties. This seems like a lot of data, but it turns out that it is equivalent to the data of a single representation of a group, the group of automorphisms of the formal d-dimensional disk. This equivalence of categories can be proved via an intermediate category, the category of quasi-coherent sheaves on a stack of ├ętale germs of d-dimensional varieties. For those who have not seen stacks in action, this is a nice and approachable example of how they can be used to organize complicated structures and answer questions which otherwise seem quite intractable. No prior knowledge of stacks will be assumed.


February 24, 2017
2:00 pm - 3:00 pm GMT
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Room 205
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