Complex K-theory of dual Hitchin systems

Michael Groechenig (University of Toronto)

07-Oct-2021, 12:00-14:00 (2 years ago)

Abstract: Let G and G’ be Langlands dual reductive groups (e.g. SL(n) and PGL(n)). According to a theorem by Donagi-Pantev, the generic fibres of the moduli spaces of G-Higgs bundles and G’-Higgs bundles are dual abelian varieties and are therefore derived equivalent. It is an interesting open problem to prove existence of a derived equivalence over the full Hitchin base. I will report on joint work in progress with Shiyu Shen, in which we construct a K-theoretic shadow thereof: natural equivalences between complex K-theory spectra for certain moduli spaces of Higgs bundles (in type A).

algebraic geometrynumber theory

Audience: researchers in the topic


Algebraic Geometry and Number Theory seminar - ISTA

Organizers: Tamas Hausel*, Tim Browning*
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