Joint IAS/PU Arithmetic Geometry

Toward Quasi-classical Fundamental Local Equivalence.

Fundamental Local Equivalence of Gaitsgory and Lurie is an instance of quantum local geometric Langlands correspondence. It asserts an equivalence between the affine category $O$ and the category of twisted Whittaker $D$-modules on the affine flag variety for the dual group. A version of this conjecture was proved by Campbell, Dhillon, Raskin. In this talk I will explain our work in progress with Dhillon where we study the quasi-classical version of this equivalence: instead of modules over quantizations the categories we care about are those of equivariant modules over suitable commutative algebras. Our main result is a construction of a functor from the category $O$ side to the Whittaker side that has several properties expected of the equivalence -- but we do not know how to prove that our functor is an equivalence. I will try to keep the exposition reasonably elementary.

The talk is based on work in progress with Gurbir Dhillon.

Date & Time

October 26, 2026 | 3:30pm – 4:30pm

Add to calendar 10/26/2026 15:30 10/26/2026 16:30 Joint IAS/PU Arithmetic Geometry use-title Topic: Toward Quasi-classical Fundamental Local Equivalence. Speakers: Ivan Loseu, Yale University More: https://www.ias.edu/math/events/joint-iaspu-arithmetic-geometry-58 Fundamental Local Equivalence of Gaitsgory and Lurie is an instance of quantum local geometric Langlands correspondence. It asserts an equivalence between the affine category $O$ and the category of twisted Whittaker $D$-modules on the affine flag variety for the dual group. A version of this conjecture was proved by Campbell, Dhillon, Raskin. In this talk I will explain our work in progress with Dhillon where we study the quasi-classical version of this equivalence: instead of modules over quantizations the categories we care about are those of equivariant modules over suitable commutative algebras. Our main result is a construction of a functor from the category $O$ side to the Whittaker side that has several properties expected of the equivalence -- but we do not know how to prove that our functor is an equivalence. I will try to keep the exposition reasonably elementary. The talk is based on work in progress with Gurbir Dhillon. Princeton University, Fine Hall 224 a7a99c3d46944b65a08073518d638c23

Location

Princeton University, Fine Hall 224

Speakers

Ivan Loseu, Yale University

Event Series

Arithmetic Geometry