Introduction and overview of symplectic geometry

Speaker：Kenji Fukaya 深谷贤治

Kenji Fukaya is a Professor at YMSC. He received his BA in Mathematics at the University of Tokyo in 1981, and continued graduate studies at the University of Tokyo, receiving his PhD in 1986. Fukaya's recent work has been in symplectic geometry and in particular has centered around the study of Lagrangian submanifolds and the Floer homology related to intersections of these submanifolds. Fukaya developed and has studied extensively a theory in which the Lagrangian submanifolds of a given symplectic manifold are the objects of a generalized category, now called the Fukaya category, and the morphisms are the Floer homology groups. Fukaya was awarded the Japan Academy Award in 2003, Asahi prize in 2009, and Fujiwara prize in 2012. He is a member of the Japanese National Academy of Sciences.

Time：

Wed. & Fri., 17:05-18:40,

Sept. 9 to Nov. 29, 2024

Venue：

C548, Shuangqing Complex Building A

Description:

This is an introductory course on the area of symplectic geometry especially global theory of symplectic manifold.

The main purpose is to provide self-contained introduction of the field and also a overview of many of its related field and recent development.

For the elementary part I plan to provide full detail of the proof. There is a technique called method of pseudo-holomorphic curve, which plays an important role in modern development of the field. I plan to survey it but for this part the lecture is rather sketchy. The full detail of pseudo-holomorphic curve theory is planned to be explained in some other lecture, likely in this or in the next year.

Prerequisite:

Basic part of manifold theory. Differential form and de-Rham's theorem.

Target Audience:

Undergraduate students, Graduate students

Teaching Language:

English