- Date : 2022-12-30 (Fri) 14:00 ~ 15:30
- Place : 27-325 (SNU)
- Speaker : Tony Yau (CUHK Hong Kong)
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TiTle : Morphism spaces between coisotropic A-branes
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Abstract :
Seeking for a mathematical definition of morphism spaces between coisotropic A-branes has been a long-standing problem for understanding mirror symmetry. In 2009, a paper of Gukov-Witten showed that this problem is also closely related to deformation quantization and geometric quantization. In this talk, I shall explain my recent joint work with NaiChung Conan Leung that for a fixed prequantum line bundle L over a hyperKahler manifold X, there is a natural but hidden Sp(1)-symmetry intertwining a twistor family of Spin^c-Dirac operators on the spaces of L-valued (0, *)-forms on X. It leads to a proposed definition of the morphism space of a brane-conjugate brane system for a space-filling coisotropic A-brane on a symplectic manifold, and it establishes geometric quantization via brane quantization on a hyperKahler manifold.