Tuesday, May 26
9.30-10.30: Šarūnas Kaubrys
10.30-11: Break
11-12: Elsa Maneval
12-2: Lunch break
2-3: David Fang
3-3.30: Break
3.30-4.30: Eric Chen
Eric Chen, EPFL
Title: Langlands functoriality of Hitchin systems
Abstract: Traditionally, Langlands functoriality refers to the identification of automorphic forms whose parameters take a special shape. In this talk, we explain how to ask analogous questions on the Hitchin moduli space using perspectives from the relative Langlands program. We gain, in this setting, the advantage of working with a version of Langlands duality which is readily computable, and if time permits we will discuss the ramifications of these calculations for automorphic periods and L-functions.
David Fang, Yale
Title: On Fourier-Mukai transforms for Hitchin systems
Abstract: In this talk we consider the moduli stack of (possibly meromorphic) semistable (GL_r)-Higgs bundles on a curve. The Dolbeault Langlands conjecture of Donagi-Pantev (later refined by Padurariu-Toda) predicts roughly the existence of an autoequivalence of the derived category of coherent sheaves on this moduli stack, which is compatible with certain classical limit Hecke and Wilson operators. In 2006, Donagi and Pantev further proposed that the kernel for such an autoequivalence may be constructed as a degeneration of the usual Poincare sheaf for Jacobians of spectral curves. In this talk we present some evidence for these conjectures, and some interactions of this equivalence with the obvious G_m-action on the moduli stack of Higgs bundles.
Šarūnas Kaubrys, IPMU
Title: Langlands duality for critical cohomology of local systems on the 3-torus and loop nonabelian Hodge theory
Abstract: In this talk I will explain a conjectural duality for critical cohomology of local systems on 3-manifolds, due to Safronov-Williams, Ben-Zvi-Jordan-Gunningham-Safronov. I will explain my work on a proof of this conjecture for the 3-torus in the type A case. We can also consider a Dolbeault version of this duality via a version of nonabelian Hodge theory for loop stacks. Finally, I will explain some work in progress towards understanding the cohomological Hall algebra structure for local systems on the 3-torus.
Elsa Maneval, EPFL
Title: Topological mirror symmetry for SL_n/PGL_n Higgs bundles
Abstract: I will first introduce the moduli spaces of Higgs bundles that appear in the Hausel-Thaddeus topological mirror symmetry conjecture, present its different proofs and generalisations. In particular I will explain the p-adic integration approach of Groechenig, Wyss and Ziegler. Finally, I will present my result, which is a generalisation beyond the original coprime case of the key intermediate step of this approach, which we call a non-archimedean topological mirror symmetry.