SLE, LOEWNER ENERGY, AND WEIL-PETERSSON QUASICIRCLES
YILIN WANG – MASSACHUSETTS INSTITUTE OF TECHNOLOGY
The Loewner energy for Jordan curves first arises from the small-parameter large deviations of Schramm-Loewner evolution (SLE), a family of random fractal curves modeling interfaces in 2D statistical mechanics. Surprisingly, a Jordan curve has finite Loewner energy if and only if it is a Weil-Petersson quasicircle, an interesting class of deterministic curves appearing in Teichmuller theory, geometric function theory, and string theory with currently more than 20 equivalent definitions. I will give an overview on these links, and show that the probabilistic SLE interpretation to classical theories generates further research directions on both sides.