Oct 20 - Eveliina Peltola, University of Bonn & Aalto University.
Title: Large deviations of SLEs, real rational functions, and zeta-regularized determinants of Laplacians
Abstract: When studying large deviations (LDP) of Schramm-Loewner evolution (SLE) curves, we recently introduced a ''Loewner potential'' that describes the rate function for the LDP. This object turned out to have several intrinsic, and perhaps surprising, connections to various fields. For instance, it has a simple expression in terms of zeta regularized determinants of Laplace-Beltrami operators. On the other hand, minima of the Loewner potential solve a nonlinear first order PDE that arises in a semiclassical limit of certain correlation functions in conformal field theory,
arguably also related to isomonodromic systems. Finally, and perhaps most interestingly, the Loewner potential minimizers classify rational functions with real critical points, thereby providing a novel proof for
a version of the now well-known Shapiro-Shapiro conjecture in real enumerative geometry. This talk is based on joint work with Yilin Wang (MIT).
Oct 27 - Matan Harel, Northeastern University.
Nov 03 - Ariel Yadin, Ben-Gurion University.
Nov 10 - Slim Kammoun, Université de Toulouse III (France).
Nov 17 - Fabio Toninelli, Technical University of Vienna.
Nov 24 - Sarah Penington, University of Bath.
Dec 01 - Ofer Zeitouni, Weizmann Institute of Science & NYU
Dec 08 - Cyril Labbé, Paris Dauphine University.
Jan 12 - Zied Ammari, Université Rennes 1.
Jan 19 - Shahar Mendelson, University of Warwick.
Oct 13 - Alexander Povolotsky, Joint Institute for Nuclear Research, Dubna, Russia.
Title: Generalized TASEP between KPZ and jamming regimes
Abstract: Totally Asymmetric Simple Exclusion Process (TASEP) with generalized update is an integrable stochastic model of interacting particles, which differs from the standard TASEP by the presence of an additional interaction controlling the degree of particle clustering. As the strength of the interaction varies, the system suffers the transition from the regime in which the fluctuations of the particle flow are described by standard random processes associated with the Kardar-Parisi-Zhang (KPZ) universality class, to the jamming regime, in which all particles stick to one cluster and move synchronously as the simple random walk. I will focus on the limiting laws of fluctuations of distances travelled by tagged particles both in the KPZ and in the transitional regime for two types of initial conditions. In particular new transitional processes interpolating between the known limiting cases will be discussed.