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.