Wednesday, January 19, 2022
Time  Items 

All day 

4:00pm 
01/19/2022  4:15pm Abstract: The Loewner energy for Jordan curves first arises from the smallparameter large deviations of SchrammLoewner 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 WeilPetersson 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, WeilPetersson quasicircles, and other branches of mathematics it touches on. I will highlight how ideas from probability theory inspire new results on WeilPetersson quasicircles and discuss further directions. Location: 