7-10【Huagui Duan】On the minimal number of closed geodesics on Finsler spheres

In this talk, we will introduce the problem about the optimal number of closed geodesics on Finsler spheres. In particular, recently it has been proved that for every Finsler metric on certain positively-curved spheres of dimension $n$, there exist at least $n$ prime closed geodesics, which solved a conjecture of Katok and Anosov for such spheres when $n$ is even, which is a joint work with Dong Xie.