Title: Conjectures of Ben Zvi--Sakellaridis--Venkatesh and Gaiotto.

Abstract:  In an ongoing project of D. Ben Zvi, Y. Sakellaridis and A. Venkatesh, the authors propose certain  Periods--L-functions duality conjectures.

In certain cases, the local version of these conjectures predicts an equivalence of categories between so-called equivariant D-modules on an affine Grassmannian and representations of a degenerate supergroup.

Gaiotto suggested a deformation of this equivalence relating the twisted equivariant D-modules on the affine Grassmannian with representations of the quantum supergroup.

In my talk I will formulate these conjectures and will report on our ongoing joint project with A.Braverman, V.Ginzburg and R.Travkin towards the proof of Gaiotto conjecture.

I will also explain some combinatorial consequences (positivity of super versions of Kostka polynomials).

Zoom link 
https://huji.zoom.us/j/83571551922?pwd=NTJqNmVGRWVpb2dxQnBWbjdoVHVHdz09

Meeting ID: 835 7155 1922
Passcode: 474769