Notes of talks

Titles of series:

GL: statement of quantum geometric Langlands;

Wh: Whittaker categories;

Ja: Jacquet functors;

Ch: Chiral algebras and factorization;

FLE: Fundamental local equivalence.

Day 1:

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

Tony Feng)

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.

T-1a: S. Raskin, Additional tutorial on actions of groups on categories

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.

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.

T-2a: D. Gaitsgory, Additional tutorial on factorization algebras and categories

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

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. (notes by

Gurbir Dhillon)

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

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:

Ja-4: J. Campbell, The semi-infinite IC sheaf; its role for the global Jacquet/Eisenstein series functors.

Ja-5: Y. Zhao, Jacquet/Eisenstein functors in the global situation and interaction with their local counterparts.

Wh-5: D. Gaitsgory, Jacquet functor of the Whittaker category–getting down to combinatorics (notes by Raeez Lorgat); (literal transcription).

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

FLE-2and3: D. Gaitsgory, Strategy of the proof of FLE via Jacquet functors; poor man’s FLE: going to the small quantum group.