Seminar on Arithmetic Geometry and Quantum Field Theory
Organisers: Jeff Harvey and Minhyong Kim
Wednesdays, 20:00 London time, approximately 30 weeks per year
If you are interested in attending this online seminar, please send an email to Minhyong Kim.
Schedule, Spring, 2021
2 June, 2021, 20:00 UK time
Vadim Schechtman (Toulouse)
Title: Conformal blocks and factorisable sheaves
Conformal blocks ("one half" of correlation functions) are solutions of certain remarkable partial
discovered by physicists in the mid-1980-ies. Soon afterwards it was found that they are
closely related to quantum groups. On the other hand these differential equations
may be expressed as a Gauss-Manin connection. This allowed one to interpret, using the
Lefschetz vanishing cycles, representations of quantum groups as (complexes of) sheaves over
I will briefly review these results which have found later on some unexpected applications.
9 June, 2021, 20:00 UK time
Roman Bezrukavnikov (MIT)
Title: Local geometric Langlands and roots of unity
Abstract: I will review relations between quantum groups at a root of unity and categories appearing in local geometric Langlands.
The talk will be based on old papers with Arkhipov, Ginzburg, Braverman, Gaitsgory and Mirkovic, and work in progress
with Boixeda Alvarez, McBreen and Yun.
16 June, 2021, 17:00 UK time
(NOTE CHANGE OF TIME!)
Mikhail Finkelberg (HSE University)
Title: Factorizable sheaves and local systems of conformal blocks
Abstract: This is a continuation of the talk of Vadim Schechtman on June 2nd. I will explain how the theory of factorizable sheaves implies the motivic property of local systems of conformal blocks of WZW models.