Talbot 2008

Mentored by Dennis Gaitsgory of Harvard

Preparation for the workshop: Chiral algebras seminar (organized by Mike Hopkins) and the MIT Pre-Talbot seminar.

The workshop schedule:

Monday

1.  Introduction/overview (Dennis Gaitsgory)

2. Overview of quantum groups (Ian Le)

   • 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 Schedler)

4. Drinfeld doubles (Nick Rozenblyum)

   • 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 Gwilliam)

   • Definition of the affine Grassmannian and how it gives a factorization space.

6. Factorization algebras and E2 algebras (John Francis or Jacob Lurie)

7. E2 modules and factorization modules (John Francis or Jacob Lurie)

8. Koszul duality, E2 algebras and Drinfeld doubles (Jacob Lurie)

Wednesday

9. D-modules (Zhiwei Yun)

10. Twistings and twisted D-modules (Reimundo Heluani)

11. Chiral categories (John Francis or Jacob Lurie)

12. Factorizable sheaves (Carl Mautner)

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 Dhand)

15. Discussion

16. The twisted Whittaker category (Xinwen Zhu)

    • Definition of the twisted Whittaker category Whitc of the affine Grassmannian

Friday

17. Construction of the functor Whitc→ FS (Scott Carnahan)

18. Proof that the functor is an equivalence (Richard Cudney)

19. TBD.