program

Tentative program (a detailed pdf file)

The talks will roughly follow five separate series:

GL: statement of quantum geometric Langlands;

Wh: Whittaker categories;

Ja: Jacquet functors;

Ch: Chiral algebras and factorization;

FLE: Fundamental local equivalence.

In addition, we will have a number of tutorials (T-series) on the background material.

Schedule

On January 15 - 16 the conference will take place in Salle des thèses HAF 580F, building "Halle aux Farines". The plan of the building "Halle aux Farines". The room HAF 580F is on the 5th floor of HALL E, the room is yelow on the plan. One need to take the staircase F1/F2 to get there.

On January 17 - 19 the conference will take place in amphi Turing, building "Sophie Germain" (see a plan of the campus on the `information for participants' page).

Talk 1: 9.30-10.30

Talk 2: 10.45-11.45

Coffee break

Talk 3: 12-13

Lunch

Talk 4: 14.30-15.30

Coffee break

Talk 5: 15.45-16.45

Talk 6: 17-18 (some days)

Program

Day 1:

GL-1: D. Gaitsgory, Introduction to quantum local geometric Langlands.

T-1: Y. Fu, Tutorial on groups acting on categories.

Wh-1: D. Beraldo, The Whittaker model.

GL-2: Y. Zhao, The quantum parameter.

GL-3: D. Arinkin, The global quantum geometric theory.

Day 2:

Ch-1: D. Gaitsgory, The factorization category of D-modules on the affine Grassmannian.

T-2: Q. Ho, Tutorial on factorization algebras and categories.

GL-4: S. Lysenko, Quantum Satake equivalence.

Wh-2: D. Beraldo, Proof of the equivalence of the two versions of the Whittaker model.

Ja-1: S. Raskin, Jacquet functors for actions of loops groups on categories.

Day 3:

T-3: J. Tao, Tutorial on the functor of weak invariants of a group acting strongly on a category.

GL-5: S. Raskin, The functor of weak L(G)-invariants.

GL-6: D. Arinkin, Spectral side in the classical case.

FLE-1: D. Gaitsgory, Statement of the equivalence; local-to-global compatibility; compatibility with quantum Satake.

Wh-3: D. Gaitsgory, Statement of local quantum Langlands.

GL-7: S. Raskin, Quantum Langlands for G being a torus.

Starting from Day 4 (with the exception of Wh-4 and Ch-3), our focus will be the FLE: its “combinatorial” nature, its relation to quantum groups, and approaches to the proof. Also, this part of the workshop will have the most concentration of concrete representation-theoretic content.

Day 4:

Ja-2: J. Campbell, Jacquet functors and Langlands duality.

T-4: S. Riche, Tutorial on quantum groups.

T-5: N. Rozenblyum, Tutorial on factorization vs braided monoidal categories.

Ch-2: D. Gaitsgory, The factorization algebra Ωq (or how Nature encodes root data).

Ja-3: L. Chen, Jacquet functor on Kac-Moody modules and the Kazhdan-Lusztig equivalence.

Wh-4: D. Yang, Duality for W-algebras.

Day 5:

Wh-5: D. Gaitsgory, Jacquet functor of the Whittaker category–getting down to combinatorics.

FLE-2: D. Gaitsgory, Strategy of the proof of FLE via Jacquet functors.

Ja-4: Y. Zhao, Jacquet/Eisenstein functors in the global situation and interaction with their local counterparts.

Ja-5: J. Campbell, The semi-infinite IC sheaf; its role for the global Jacquet/Eisenstein series functors.

FLE-3: D. Gaitsgory, Poor man’s FLE: going to the small quantum group.

Ch-3: D. Yang, The ”Master” chiral algebra.