Talbot 08 Schedule Schedule of the 2008 Talbot workshop:

Monday Tuesday Wednesday Thursday Friday

Introduction/Overview


Affine grassmannian and factorization


D-modules


Reps of quantum groups = FS


Constructing the functor


Intro to quantum groups


Factorization algebras and E2 algebras


Twistings and twisted D-modules


More affine grassmannian


Proof of equivalence


Rep theory for quantum groups


E2 modules and factorization modules


Chiral categories


discussion session


TBD


Drinfeld doubles


Koszul duality, E2 algebras, and Drinfeld doubles


FS category


The twisted Whittaker category


discussion session



-- Monday --

1. Introduction/Overview. [Dennis Gaitsgory]


2. Overview of quantum groups. [Ian]
Definition of quantum universal enveloping algebras Uq(g); the structure of its category of representations -- braided and ribbon tensor structure and R-matrix; the big and small quantum group, at and away from roots of unity.

3. Representation theory for quantum groups. [Travis]


4. Drinfeld doubles. [Nick]
Show the equivalence DD(Uq(n+)) = Rep Uq(g) away from roots of unity, and fully faithful embedding at roots of unity.

-- Tuesday --

5. Affine grassmannian and factorization structures. [Owen]
Definition of the affine grassmannian. How it gives a factorization space.

6. Factorization algebras and E2 algebras. [John or Jacob]

7. E2 modules and factorization modules. [John or Jacob]

8. Koszul duality, E2 algebras and Drinfeld doubles. [Jacob]

-- Wednesday --

9. D-modules. [Zhiwei]

10. Twistings and twisted D-modules. [Reimundo]

11. Chiral categories. [Jacob or John]

12. Factorizable sheaves. [Carl]

-- Thursday --

13. Why FS is the same as chiral modules for the partial Koszul dual of Uq(n+). [Dennis Gaitsgory]

14. More affine grassmannian. [Vivek]

15. Discussion.

16. The twisted Whittaker category. [Xinwen]
Definition of the twisted Whittaker category Whitc of the affine Grassmannian.

-- Friday --

17. Construction of the functor Whitc → FS. [Scott]
What it says.

18. Proof that the functor is an equivalence. [Richard]
Ditto.

19. TBD.
...