## Graduate Seminar in Geometric Representation theory.

Spring 2012

For the first half of the semester the seminar will focus on the point of view on the category
of representations

of the Quantum Group via factorization. In the process we will
recover the Finkelberg-Schechtman equivalence

between u_q-mod with the category
of factorizable sheaves, and the Schechtman-Varchenko picture for U_q(n)

as
cohomology of certain local systems on configuration spaces.

The ultimate goal is to
use this point of view to connect with representations of affine algebras at the negative
level

and thereby reprove the KL equivalence.

For the first few weeks the material will have a significant intersection with what
was discussed at the Talbot

workshop in 2008. Some notes are available, see link below.
### Announcements

There will be no seminar on march 27 due to the MIT spring break

### Schedule

The seminar will meet on Tuesdays 5.30-7pm for a lecture, alternating between Harvard and MIT,

and on Thursdays
at 5.30pm for a discussion/Q&A session in D.G.'s office, SC 338.

Lecture 1: Feb. 7, 5.30pm, Harvard SC 507. Dennis Gaitsgory. Overview of the theory.

Lecture 2: Feb. 14, 5.30pm, MIT, room 2-190. Dennis Gaitsgory. Factorizable gerbes.

Lecture 3: Feb. 21, 5.45pm, MIT, room 2-190. Jacob Lurie. Factorization structures in the topological setting.

Lecture 4: Feb. 28, 5.30pm, Harvard SC 507. Jacob Lurie. Factorization structures in the topological setting-II.

Lecture 5: March 6, 5.30pm, MIT, room 2-190. Jacob Lurie. Factorization structures in the topological setting-III.

Lecture 6. March 20, 5.30pm, Harvard, SC 507. Jacob Lurie. Koszul duality for factorization algebras.

Lecture 7. April 3, 5.30pm, MIT, room 2-190. Dustin Clausen. Koszul duality and Verdier duality.

Lecture 8. April 10, 5.30pm, Harvard, SC 507. Sasha Tsymbaliuk. Introduction to quantum groups.

Lecture 9. April 17, 5.30pm, MIT, room 2-190. Dennis Gaitsgory. Factorization algebras attached to Quantum Groups.

Lecture 10. April 24, 5.30pm, Harvard, SC 507. Dennis Gaitsgory. Factorization algebras attached to Quantum Groups, continued.
### Notes