学术报告

走向现代数学学术报告 - 刘会教授(No. 512)

题目:Reeb dynamics on contact three manifold with exactly two periodic orbits

报告人: 刘会 教授(武汉大学)

报告时间:2022年5月12日,16:00

报告腾讯会议号:125-189-805

摘要:In this talk I will present a complete characterization of Reeb flows on closed 3-manifolds with precisely two periodic orbits. The main step consists in showing that a contact form with exactly two periodic Reeb orbits is non-degenerate and the two orbits are irrationally elliptic. Our results are important ingredients in the recently proof of $C^2$-stability conjecture for Riemannian geodesic flows of closed surfaces by Contreras and Mazzucchelli, and the proof of the $C^\infty$ generic existence of positive topological entropy for Reeb flows on closed 3-manifolds by Colin, Dehornoy, Hryniewicz and Rechtman. I will give some explanations how our results can be applied to their proofs.  This talk is based on my joint work with Cristofaro-Gardiner, Hryniewicz and Hutchings .

报告人简介:刘会,武汉大学数学与统计学院教授,博士生导师。2012年博士毕业于南开大学陈省身数学研究所,2012年至2016年在中国科学技术大学做博士后研究并任副研究员职位,2016年至今任职于武汉大学。研究领域为哈密顿动力系统,非线性分析与辛几何,主要研究兴趣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Geom. Topol., Adv. Math, J. Funct. Anal., Calc. Var. PDEs, J. Diff. Equ.等数学期刊上接受或发表论文20余篇,主持或完成国家基金委优秀青年基金、面上项目、青年基金等课题三项。