一、题目：

The closed geodesic problems on Riemannian and Finsler manifolds

二、主讲人：

刘磊

三、摘要：

The closed geodesics are the most common objects between Geometry and Dynamics area, which play an important role during the development of mathematics. In this talk, I will try to tease out all the previous researches of closed geodesic problems in different point of views. Many famous theories will be touched, such as the min-max method, Morse theory, Index theory and so on. But, since I will focus the closed geodesic problems themselves, there will be no much details included.

References:

[1] W. Klingenberg, Lectures on closed geodesics, Springer. Berlin. 1978.

[2] J. Franks, Geodesics on S2 and periodic points of annulus homeomorphisms. Invent. Math. 108(1992) 403-418.

[3] V. Bangert, On the existence of closed geodesics on two-spheres. Internet. J. Math. 4(1993) 1-10.

[4] V. Bangert, Y. Long, The existence of two closed geodesics on every Finsler 2-sphere. Math. Ann. 346(2010) 335-366.

[5] Y. Long, Multiplicity and stability of closed geodesics on Finsler 2-spheres. J. Europe. Math. Social. 8(2006) 341-353.

[6] A. Katok, B. Hasselbaltt, Introduction to the Modern Theory of Dynamical Systems, Cambridge University Press,1995.

[7] K. Irie, Dense existence of periodic reeb orbits and ECH spectral invariants, J. Mod. Dynamics. 9(2015), 357-363.

[8] D. Chen, On the C^\infty closing lemma for Hamiltonian flows on symplectic 4-manifolds, arXiv:1904.09900v1.

四、主讲人简介：

刘磊，北京国际数学研究中心

五、邀请人：

胡锡俊 数学学院教授

六、时间：

4月25日（周一）10:00-11:00

七、地点：

腾讯会议

八、联系人：

徐梦瑞，联系方式：xumr@mail.sdu.edu.cn

九、主办方：

山东大学数学学院