Higgs26: Langlands duality for critical cohomology of local systems on the 3-torus and loop nonabelian Hodge theoryWorkshop

by Šarūnas Kaubrys (IPMU)

Tuesday May 26, 2026, 9:30 AM → 10:30 AM Europe/Berlin

Endenicher Allee 60, R. 0.008 (Mathezentrum)

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.