## 3-Manifold Seminar: Schwarzian derivatives, projective structures, and the Weil-Petersson gradient flow for renormalized volume

Seminar | October 31 | 2:10-3:30 p.m. | 740 Evans Hall

Franco Vargas, UCB

Department of Mathematics

In this talk I will discuss the paper of Bridgeman, Brock and Bromberg of the same title. In this article, the authors bound both the geometry of a projective structure over a surface Σ and its associated locally convex pleated surface by norms of $\phi _\Sigma$ (the quadratic holomorphic differential given by the Schwarzian derivative). We will discuss these terms and how they relate between them. We will also see how these bounds can be use to study the Weil-Petersson gradient flow of the Renormalized Volume (after fixing a hyperbolic compact manifold N with incompressible boundary) and obtain that its infimum is equal to half the simplicial volume the double of N.

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