Mathematics Graduate Student Colloquium

MGSC Website: http://math.uci.edu/~mgsc/

Deformation Quantization of Vector Bundles on Lagrangian Subvarieties

Taiji Chen
Tuesday, May 29, 2018
4:00 pm - 4:50 pm
RH 440R

Talk Abstract:

We consider a smooth subvariety Y in a smooth algebraic variety X with an algebraic symplectic form ω. Assume that there exists a deformation quantization Oh of the structure sheaf OX. When Y is Lagrangian, for a vector bundle E on Y, we establish necessary and sufficient conditions for the existence of the deformation quantization of E. If the necessary conditions hold, we describe the set of equivalence classes of such quantizations. In the more general situation when Y is coisotropic, we reformulate the deformation problem into the lifting problem of torsors. We expect a deformation quantization of line bundles on coisotropic subvarieties is equivalent to a solution of curved Maurer-Cartan equation of a curved L-infinity algebra.

About the Speaker:

Taiji is a sixth year PhD student.

Refreshments:

Pizza will be served after the talk.