中国科学院数学与系统科学研究院

数学研究所

数学科学全国重点实验室

综合报告会

（Colloquium）

Speaker: Mohammed Abouzaid  (斯坦福大学)

Inviter: 周正一

Language: English

Title：The road from celestial mechanics to orbifold bordism

Time&Venue：2025年10月29日（星期三）15:30-17:00 & 晨兴110

Abstract: The 19th century saw tremendous achievements in celestial mechanics, leading to the discovery of Neptune. Further progress was then stymied by the gradual understanding that small denominators in approximations to the equations of motions lead to numerical instability, eventually culminating in Poincare discovery that the 3-body system is, in modern terms, chaotic. This motivated Poincare to turn towards a quest to understand quantitative features of dynamical systems, and he succeeded, in the lowest dimension, with the formulation of his last geometric problem, later proved by Birkhoff. Arnol'd understood that symplectic topology provides the proper context for extending these questions to higher dimensions. The first proof of Arnold's conjecture beyond a few specialised cases had to wait until the breakthrough of Floer homology, extending Morse-theoretic methods to settings where both ascending and descending manifolds are infinite dimensional. After providing the above context, I will explain how the connection of Morse theory with differential topology thus leads to unexpected links between the study of conservative dynamical systems and bordism theory.

Speaker Profile：Mohammed Abouzaid，美国数学家，现任美国斯坦福大学教授，此前任教于美国哥伦比亚大学。Abouzaid教授2007年毕业于芝加哥大学，并在2007-2012年获得Clay数学研究所研究资助。他在Arnold领域拉格朗日子流形猜想、wrapped Fukaya categories、Fukaya category的生成元以及近期的Floer同伦论和virtual fundamental cycles等方向上获得了一系列令人瞩目的进展。Abouzaid教授曾在2014年ICM上作45分钟报告，并获得2017年新视野奖。