7. Oct 2021

Complex K-theory of dual Hitchin systems

ALGEBRAIC GEOMETRY & NUMBER THEORY SEMINAR

Datum: 7. October 2021 | 14:00 – 16:00
Sprecher: Michael Groechenig, University of Toronto
Veranstaltungsort: https://mathseminars.org/seminar/AGNTISTA

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).