理学院学术报告20200618
发布人:何杰  发布时间:2021-06-08   浏览次数:25

Closed geodesics on Finsler compact non-simply connected manifolds


刘会  教授/博导


武汉大学




报告时间:2021618日 14:30

报告地点:核工楼1216


摘要:

For many years, there seem to be very few works on the multiplicity of closed geodesics on non-simply connected manifolds, the main reason is that the topological structures of the free loop spaces on these manifolds are not well known, so that the classical Morse theory is difficult to be applicable. In recent years, motivated by the studies on simply connected manifolds and closed characteristics on Hamiltonian energy surfaces, we study the topological structure of the contractible component and non-contractible component of the free loop space on Finsler real projective space and compact space form, which are typically non-simply connected manifolds, and then we establish some new resonance identities, which are successfully applied to get many multiplicity results of closed geodesics on these non-simply connected manifolds. In this talk, I will give a survey of our results.

 

 


报告人介绍:刘会,武汉大学数学与统计学院教授,博士生导师。研究领域为哈密顿动力系统,非线性分析与辛几何,主要研究方向为哈密顿系统与辛几何中周期轨道的多重性与稳定性等相关问题。已在Adv. Math, J.Func.Anal., Calc. Var.PDEs, J. Diff. Equa.等国际期刊上发表论文20余篇,2020年获国家优秀青年基金资助。