中科院数学与系统科学研究院
数学研究所
动力系统研究中心
学术报告会
报告人： Dr. Chi Nguyen(Laboratoire MAPMO, Université d'Orléans, France)
题 目：Coefficient problem of whole-plane SLE & LLE
时 间：12.02（星期二）, 14:30--16:00
地 点：数学院南楼N902室
摘要：
Karl Löwner (later known as Charles Loewner) introduced his famous differential equation in 1923 in order to solve the Bieberbach conjecture for series expansion coeffcients of univalent analytic functions at level n = 3. His method was revived in 1999 by Oded Schramm when he introduced the Stochastic Loewner Evolution (SLE), a conformally invariant process which made it possible to prove many predictions from conformal field theory for critical planar models in statistical mechanics. The aim of this work is to revisit the Bieberbach conjecture in the framework of SLE processes and, more generally, Lévy processes. The study of their unbounded whole-plane versions leads to a discrete series of exact results for the expectations of coefficients and their variances, and, more generally, for the derivative moments of some prescribed order p. These results are generalized to the "oddiffied" or m-fold conformal maps of whole-plane SLEs or Lévy-Loewner Evolutions (LLEs).
