Loewner Dynamics of the Multiple SLE(0) Process


Recently Peltola and Wang introduced the multiple SLE(0) process as the deterministic limit of the random multiple SLE(kappa) curves as kappa goes to zero. They also showed that the limiting curves have important geometric characterizations that are independent of their relation to SLE - they are the real locus of real rational functions, and they can be generated by a deterministic Loewner evolution driven by multiple points. We prove that the Loewner evolution is a very special family of commuting SLE(0, rho) processes. We also show that our SLE(0, rho) processes lead to relatively simple solutions to a particular high-dimensional system of quadratic equations called the degenerate BPZ equations. In addition, the dynamics of these poles and critical points come from the Calogero-Moser integrable system. Although our results are purely deterministic they are motivated by taking limits of probabilistic constructions in conformal field theory.

Apr 19, 2024 10:00 -0800 — Apr 20, 2024 11:00 -0800
University of Denver (online)
Denver, Colorado
Tom Alberts
Tom Alberts
Associate Professor of Mathematics
University of Utah
Sung-Soo Byun
Sung-Soo Byun
Assistant Professor of Mathematics
Seoul National University
Nikolai Makarov
Nikolai Makarov
Professor of Mathematics