Explore a 57-minute conference talk delivered by Martin Bridgeman from Boston College at the Instituto de Matemática Pura e Aplicada, focusing on Loewner Energy, Renormalized Volume and their Weil-Petersson gradient flows. Part of a broader conference on hyperbolic geometry and hyperbolic group theory, this presentation contributes to recent developments in the field alongside talks from 19 other distinguished speakers. The conference, organized in partnership with the Clay Mathematics Institute and the NSF, was followed by a workshop featuring three minicourses aimed at graduate students, providing in-depth introductions to key topics including exotic negatively curved manifolds, building hyperbolic manifolds with Coxeter polytopes, and arithmetic hyperbolic manifolds and their totally geodesic submanifolds.