Colloquium Series Seminar

A Jordan curve is a simple loop on the sphere. We recently introduced the conformally invariant Loewner energy to measure the roundness of a Jordan curve. Initially, the definition is motivated by describing asymptotic behaviors of Schramm-Loewner evolution (SLE), a probabilistic model of random curves of importance in statistical mechanics. Intriguingly, this energy is shown to be finite if and only if the curve is a Weil-Petersson quasicircle, an interesting class of Jordan curves that has more than 20 equivalent definitions arising in very different contexts, including Teichmueller theory, geometric function theory, hyperbolic geometry, and string theory and is studied since the eighties. The myriad of perspectives on this class of curves is both luxurious and mysterious. In my talk, I will overview the basics of Loewner energy, SLE, and Weil-Petersson quasicircles and show you how ideas from probability theory inspire many new results on Weil-Petersson quasicircles. Speaker(s): Yilin Wang (MIT)