SLE, energy duality, and foliations by Weil-Petersson quasicircles

11.01.2023 16:45 - 17:45

Yilin Wang (IHES)

Abstract: The small parameter large deviation principle of SLE gives rise to the Loewner energy, a quantity associated with a Jordan curve, as the rate function. The Loewner energy is finite if and only if the curve is a Weil-Petersson quasicircle, a class of Jordan curves that also appears in Teichmuller theory and has more than 20 equivalent definitions. 

In this talk, I will focus on the large-parameter large deviation principle of SLE.  It gives rise to a new Loewner-Kufarev energy as the rate function, which is dual to the Loewner energy via foliations by Weil-Petersson quasicircles and exhibits remarkable symmetries. The energy duality is inspired by SLE duality. This is joint work with Fredrik Viklund.

M. Beiglböck, N. Berestycki, L. Erdös, J. Maas, F. Toninelli, E. Schertzer
HS 21, HP, Stiege 8, Hauptgebäude, Universitätsring 1