Yilin Wang: The Loewner energy of a simply connected domain on the Riemann sphere

Loewner's equation provides a way to encode a simply connected domain via a real-valued driving function of its boundary. The Loewner energy of the domain is the Dirichlet energy of the driving function. It depends a priori on the parametrization of the boundary. However it was shown previously that there is no such dependence. In this talk I will present an intrinsic interpretation of the Loewner energy and a characterization of finite energy domains.