EVENT DETAILS AND ABSTRACT

Title: Marked length pattern rigidity
Speaker: Yanglong Hao
Speaker Info:
Brief Description:
Special Note: Chicago Action Now
Abstract:

Given a closed Riemannian manifold M, the length of shortest geodesic for each free homotopy class of loops on M is called the (minimal) length of the class. This gives a map called marked length spectrum. It is conjectured that the fundamental group and marked length spectrum together determine the isometric type of negatively curved manifolds. This conjecture has been verified for surfaces and locally symmetric spaces. In this talk, we show that for negatively curved arithmetic manifolds, the fundamental group together with all pair of different equal length classes is enough to recover the metric up to scaling.