The Loewner Energy at the Crossroad of Random Conformal Geometry - Lecture 2

Explore a comprehensive lecture on the Loewner energy for Jordan curves and its connections to various mathematical fields. Delve into the origins of this concept from the large deviations of Schramm-Loewner evolution (SLE) and its role in measuring the roundness of Jordan curves. Discover the relationship between finite Loewner energy and Weil-Petersson quasicircles, and learn about its connection to determinants of Laplacians. Examine the Loewner energy's function as a Kahler potential on the Weil-Petersson Teichmueller space. Investigate the intriguing class of finite energy curves with over 20 equivalent definitions spanning diverse mathematical contexts, including Teichmueller theory, geometric function theory, hyperbolic geometry, and spectral theory. Gain insights into the links between Loewner energy, SLE, and Weil-Petersson quasicircles, while exploring how ideas from random conformal geometry inspire new findings in related fields. Presented by Yilin Wang from the Institut des Hautes Etudes Scientifiques (IHES), this 1 hour and 53 minutes lecture offers a deep dive into the multifaceted nature of Loewner energy and its far-reaching implications in mathematics.