Speaker:	Tony Yau
Title:	Brane quantization and SYZ mirror symmetry
Date (JST):	Thu, May 14, 2026, 15:30 - 17:00
Place:	Seminar Room A
Abstract:	Coisotropic A-branes were introduced by Kapustin and Orlov to enlarge the Fukaya category of a symplectic manifold in a way that aligns with predictions from homological mirror symmetry. From a mathematical perspective, however, the categorical framework governing such branes remains largely undeveloped. In this talk, I focus on the semi-flat SYZ mirror symmetry setting and present a mathematical realization of the self-Hom spaces of semi-affine, space-filling coisotropic A-branes (based on joint work in progress with K. Chan, N. C. Leung, Q. Li, and Y.-H. Suen). Our construction yields a non-formal holomorphic deformation quantization of the underlying A-model manifold. This approach not only reflects ideas from the Gukov–Witten brane quantization proposal and the family Floer theory framework, but also leads to a mirror correspondence identifying these A-model morphism spaces with the corresponding B-model morphism spaces on the mirror manifold. Moreover, the resulting actions on Lagrangian A-branes supported on torus fibers, and on their mirror B-branes, are shown to be functorial.

← Back