Motives and (super-)representation theory: principles and case studies
De Yves André
Finiteness Questions for Étale Coverings with Bounded Wild Ramification at the Boundary
De Vasudevan Srinivas
Apparaît dans la collection : Summer School 2021: Enumerative Geometry, Physics and Representation Theory
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).