Topology Seminar

Date: October 6, 2021

Time: 4:00PM - 5:00PM

Location: Zoom

Speaker: Shu Shen, Sorbonne University

Title: The Fried conjecture for admissible twists

Abstract: 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 of the Laplacians, equals the zero value of the dynamical zeta function. In this talk, I will show the Fried conjecture on locally symmetric spaces twisted by an acyclic flat vector bundle obtained by the restriction of a representation of the underlying Lie group. This generalises the results of myself for unitary twists, and the results of Brocker, Muller, and Wotzker on closed hyperbolic manifolds.