报告摘要：At the beginning of the 20th century, H. Poincaré and G. D. Birkhoff gave profound contributions to the qualitative theory of dynamical systems motivated by their studies in Celestial Mechanics. Their fixed point theorem eventually inspired many conjectures on Hamiltonian dynamics, culminating in the development of new methods in Symplectic and Contact Topology. In this talk, I will revisit some classical results of Hamiltonian dynamics in light of these new methods, particularly using pseudo-holomorphic curves. I will discuss a generalization of the Poincaré-Birkhoff fixed point theorem for Reeb flows on the tight 3-sphere and also general results on the existence of global surfaces of section and transverse foliations.

报告人简介：Salomão教授是巴西圣保罗大学教授，现任上海纽约大学访问教授。他的主要研究领域为动力系统与辛几何，在哈密顿系统、Reeb流、Systolic不等式等重要的几何——动力系统问题上做出了卓越贡献。Salomão教授曾获德国洪堡基金会Friedrich Wilhelm Bessel Research Award、巴西数学会奖等奖励，曾任Simons访问教授职位，在普林斯顿高等研究院、波鸿鲁尔大学、上海纽约大学等学府访问，并在2018年国际数学家大会做受邀报告。Salomão教授共发表研究论文三十篇，见刊于Invent. Math., Astérisque, Duke Math. J., Proc. London Math. Soc., JEMS, Math. Ann., Compositio等知名期刊。