Speaker: Yutung Yau (Chinese University of Hong Kong)
Time: 2025-07-11 14:00
Location: R1610,SIMIS
Zoom Meeting ID: 830 8899 6892 (Passcode: 164057)
Abstract:
Consider a spin Kahler 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 O^(k)_qu of smooth functions on M with a non-formal star product and a left O^(k)_qu -module structure on the sheaf of holomorphic sections of L^k⊗√K. 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 O^(k)_qu -\bar{O}^(k)_qu bimodule structure on the sheaf of smooth sections of L⊗2k to realize the actions of Hom(Bcc, Bcc) and Hom(\bar{Bcc}, \bar{Bcc}) on Hom(\bar{Bcc}, Bcc).
About Speaker:
Yutung Yau is currently a visiting scholar at the Institute of Mathematical Sciences, the Chinese University of Hong Kong. He completed his PhD at the Chinese University of Hong Kong under the supervision of Prof. Conan Leung. Prior to joining IMS, he held a Postdoctoral Assistant Professor position at the University of Michigan.
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