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.

Past Events


Schedule, Spring, 2021




2 June, 2021, 20:00 UK time

Vadim Schechtman (Toulouse)

Title: Conformal blocks and factorisable sheaves

Abstract: Conformal blocks ("one half" of correlation functions) are solutions of certain remarkable partial differential equations 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 configuration spaces. I will briefly review these results which have found later on some unexpected applications.

Slides

Video


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.