Title：Quantitative characterizations in Hamiltonian dynamics

Abstract：Persistence module theory is a newly-developed theory from applied algebraic topology. It enriches the classical homological theory by allowing homologically invisible generators (or called torsions) to be considered. This leads to various surprising applications in topology, analysis, and dynamics. In this talk, we will review the main results of persistence module theory, and elaborate on several recent applications in Hamiltonian dynamics and classical differential geometry. In particular, we will see how the information from torsions in Floer homology and loop space homology leads to novel results on closed orbits in the Hamiltonian sense and in the geodesics sense.

报告人简介：张俊博士毕业于美国佐治亚大学，并在以色列特拉维夫大学和加拿大蒙特利尔大学-CRM研究所完成了博士后工作，于2022年加入中国科学技术大学-几何与物理研究中心，任助理教授一职。张俊博士的主要研究方向为辛几何，具体涉及哈密尔顿动力系统，切触几何以及微局部分析。目前，张俊博士已有十余篇文章发表在国际核心期刊，包括Geometry&Toplology, Journal of Symplectic Geometry, Communications in Contemporary Mathematics等。另外，张俊博士还有两部前沿学术专著，分别由美国数学学会和Springer出版。

报告时间：2023年4月11日（周二）16:10-17:10

报告地点：知新楼B924

邀请人：况闻天副研究员