On large deviations of SLEs, real rational functions, and zeta-regularized determinants of Laplacians

When studying large deviations (LDP) of Schramm-Loewner evolution (SLE) curves, a ''Loewner energy", and "Loewner potential'', that describe the rate function for the LDP, were recently introduced. While these objects were originally derived from SLE theory, they turned out to have several intrinsic, and perhaps surprising, connections to various fields. I will discuss some of these connections and interpretations towards Brownian loops, semiclassical limits of certain correlation functions in conformal field theory, and rational functions with real critical points (Shapiro-Shapiro conjecture in real enumerative geometry).

(Based on joint work with Yilin Wang - IHES, France.)