Michael Groechenig: Complex K-theory of dual Hitchin systems
2021-10-07 14:00 - 16:00 | https://mathseminars.org/seminar/AGNTISTA, ISTA
Speaker: Michael Groechenig
hosted by Tamas Hausel
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).
