10 May 2022
10:00 am - 11:00 am
Tuesday, 10 May @ 1000 (AEST) (Melbourne)
Tuesday, 10 May @ 0800 (CST) (Beijing)
Tuesday, 10 May @ 0530 (IST) (New Delhi)
Tuesday, 10 May @ 0100 (BST) (London)
Monday, 9 May @ 2000 (EDT) (New York)
Monday, 9 May @ 1700 (PDT) (Berkeley)
Presenter: Dr Yilin Wang, MIT
Yilin is a Strauch Postdoctoral fellow at MSRI and C.L.E. Moore Instructor at MIT since 2019. She is currently working on topics at the interface of Complex analysis and Probability theory. Her current research focuses on themes that aim at enlightening the connections among Random conformal geometry, Geometric function theory, and Teichmueller theory. Yilin is a 2022 Maryam Mirzakhani New Frontiers Prize winner.
Title: How round is a Jordan curve?
Abstract: 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. In a certain way, this energy measures the roundness of a Jordan curve, and we show that it is finite if and only if the curve is a Weil-Petersson quasicircle. This class of curves has intriguingly more than 20 equivalent definitions arising in very different contexts, including Teichmueller theory, geometric function theory, hyperbolic geometry, spectral theory, and string theory, and has been studied since the eighties. The myriad of perspectives on this class of curves is both luxurious and mysterious. I will overview the links between Loewner energy and SLE, Weil-Petersson quasicircles, and other branches of mathematics it touches on.
Structure: 45 minutes seminar with 15 minutes question time
Seminar Recording and Slides: