题目：A review of the index method in closed geodesic problem

时间：2024年5月8日（周三）15:00-17:00

腾讯会议：665-472-429

报告人：王嵬 教授 北京大学

摘要：

In this report we review and systematize the index method in closed geodesic problem. As we know, the closed geodesic problem on compact Riemannian or Finsler manifold is a famous problem, and has far from been resolved. In recent years, the Maslov-type index theory for symplectic path has been applied to studying the closed geodesic problem, and has induced a great number of results on the multiplicity and stability of closed geodesics. We will systematically introduce these progresses in this review.

报告人简介：

王嵬，北京大学数学学院教授，国家杰出青年科学基金获得者。主要研究辛几何中非线性哈密顿系统的周期轨道和微分几何中的闭测地线问题。在哈密顿系统的研究中，单独或与人合作分别证明当n=4或3时，任何R^2n中的紧凸超曲面上一定存在至少n个闭特征，这对n=4, 3 的情形解决了哈密顿分析中的一个源自1892年Liapunov时期的长期猜想。在闭测地线方面，证明在一定(generic)条件下Anosov在1974年的ICM上提出的一个猜想。相关研究成果发表在Duke Math. J., Adv. Math. , J. Eur. Math. Soc., J. Differential Geom.，Calc. Var. Partial Differential Equations 等国际著名数学杂志。