EVENT DETAILS AND ABSTRACT

Title: An Inverse Problem for Renormalized Area/Entanglement Entropy
Speaker: Jared Marx-Kuo
Speaker Info: Stanford University
Brief Description:
Special Note:
Abstract:

Many inverse problems focus on determining the metric, g, given some set of information, e.g. the distance between any two boundary points. In an asymptotically hyperbolic (AH) setting, a topological boundary exists, but the distance between any two such points is infinite. In 2017, Graham-Guillarmou-Stefanov-Uhlmann showed that a "renormalized length" of geodesics between any two points on the boundary of an AH manifold determines the asymptotic expansion of the metric near the boundary.

In this talk, we generalize the above result but using the conformally invariant "renormalized area" of minimal surfaces in AH spaces. In particular, we are able to recover the conformal infinity of the metric, as well as the asymptotic expansion of the metric. As an application, we can determine the conformal structure of a hyperbolic 3-manifold, as well as the non-local term in the expansion of a Poincare-Einstein metric.