题目：Analytic torsion and dynamical zeta function on closed locally symmetric spaces.
时间：7月21日 周四 下午5:00-6:30
摘要: The relation between the spectrum of the Laplacian and the closed geodesics on a closed Riemannian manifold is one of the central themes in differential geometry. Fried conjectured that the analytic torsion, which is an alternating product of regularized determinants ofthe Hodge Laplacians, equals the zero value of the dynamical zeta function. In the first part of the talk, we will give a formal proof of this conjecture based on the path integral and Bismut-Goette’s V-invariants. In the second part, we will give the rigorous arguments in the case where the underlying manifold is a closed locally symmetric space. The proof relies on the Bismut’s formula for semisimple orbital integrals. This talk is based on a recent preprint arXiv:1602.00664.