Nov

8

2024

When:
Friday, November 8, 2024

3:00 PM - 4:00 PM CT

Where: Lunt Hall, 104, 2033 Sheridan Road, Evanston, IL 60208 map it

Audience: Faculty/Staff - Student - Public - Post Docs/Docs - Graduate Students

Contact:
Eric Zaslow
(847) 467-6447

Group: Department of Mathematics: Geometry/Physics Seminar

Category: Lectures & Meetings

**Title:** Higher rank brane quantization of Kaehler manifolds

**Abstract:** Consider a spin Kaehler manifold M with a prequantum line bundle L. Gukov-Witten suggested that, with respect to the A-model on a complexification X of M, the morphism spaces Hom(Bcc, Bcc) and Hom(B, Bcc) should recover holomorphic deformation quantization of X and geometric quantization of M respectively, where Bcc is a canonical coisotropic A-brane on X and B is a Lagrangian A-brane supported on M.

On the other hand, Chan-Leung-Li adopted Fedosov's gluing argument to construct a dense subsheaf Oqu of smooth functions on M with a non-formal star product and a left Oqu-module structure on the sheaf of holomorphic sections of the tensor product of kth tensor power of L and a square root of the canonical bundle of M.

In this talk, I will discuss the relation between (holomorphic) deformation quantizations of M and a sufficiently small complexification X so as to verify that Chan-Leung-Li's construction provides a mathematical realization of the action of Hom(Bcc, Bcc) on Hom(B, Bcc). I will also introduce a categorification of their construction and propose that it serves as part of the categorical structures on higher rank coisotropic A-branes on X, motivated by Kuwagaki's idea of sheaf quantization.

**Please note:** special day, time and location