## Topology Seminar (Main Talk): Bounds on renormalized volume and the volume of the convex core

Seminar | February 28 | 4-5 p.m. | 3 Evans Hall

Ken Bromberg, University of Utah

Department of Mathematics

A conformally compact hyperbolic 3-manifold will have infinite volume (at least if the conformal boundary is non-empty). Krasnov and Schlenker defined a renormalized volume (motivated by work of Graham and Witten on conformally compact Einstein manifolds) that assigns a finite volume to such manifolds. This defines a function on the space of all conformally compact hyperbolic 3-manifolds. We will discuss the gradient flow of this function which seems to reveal, in ways will make precise, the geometry of the manifolds. In particular, we will show how this gradient flow can be used to give bounds on the volume of the convex core of the manifolds. This is joint work with M. Bridgeman and J. Brock.

c_abbott@berkeley.edu