The Loewner Energy at the Crossroad of Random Conformal Geometry - Lecture 1

Explore the intricate connections between the Loewner energy for Jordan curves and various branches of mathematics in this comprehensive lecture. Delve into the origins of Loewner energy 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 fascinating class of finite energy curves with over 20 equivalent definitions spanning 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 concepts from random conformal geometry inspire new findings in related mathematical fields.