Topic: Open closed Gromov-Witten-Floer theory and its application

Speaker: Prof. Kenji Fukaya

Host: Prof. Xue Feng Wang

Date: Friday, Oct.17, 2025

Time: 10:30 a.m. - 11:45 a.m.

Venue: SIN Wai Kin International Conference Centre (W201), Administration Building

Language: English

Abstract: 

Gromov-Witten invariant studies counts of holomorphic map from closed Riemann surface to a symplectic manifold. A version of Floer homology is related to the count of holomorphic disks with boundary conditions in symplectic manifold. They are related and its relation is important for various purposes such as mirror symmetry.

Together with M. Abouzaid, Y.-G. Oh, H. Ohta, K. Ono we are supposed to write a paper (or a book) on this topic. It was first announced 10 years ago. Now we are completing it. I want to explain some of the contents of that research.

Speaker’s Profile:

Kenji Fukaya is currently a Professor at the Yau Mathematical Sciences Center (YMSC) at Tsinghua University. Previously, he held academic positions at the University of Tokyo, Kyoto University, and the Simons Center for Geometry and Physics at Stony Brook University.

Fukaya's research is primarily in symplectic geometry, with a focus on Lagrangian submanifolds and Floer homology. He is renowned for developing the Fukaya category, in which Lagrangian submanifolds of a symplectic manifold serve as objects and the morphisms are given by Floer homology groups. This work is closely related to Kontsevich's homological mirror symmetry conjecture.

Fukaya is a member of the Japan Academy of Sciences and has received numerous prestigious awards worldwide – most recently the Shaw Prize in Mathematical Sciences in 2025.