• CARMA COLLOQUIUM
  • Speaker: Michael Kozdron, Department of Mathematics & Statistics , University of Regina
  • Title: A Random Look at the Schramm-Loewner Evolution
  • Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 4:30 pm, Thu, 7th Apr 2011
  • Please note the variation from our usual colloquium time.
  • Abstract:

    The stochastic Loewner evolution (SLE) is a one-parameter family of random growth processes in the complex plane introduced by the late Oded Schramm in 1999 which is predicted to describe the scaling limit of a variety of statistical physics models. Recently a number of rigorous results about such scaling limits have been established; in fact, Wendelin Werner was awarded the Fields Medal in 2006 for "his contributions to the development of stochastic Loewner evolution, the geometry of two-dimensional Brownian motion, and conformal field theory" and Stas Smirnov was awarded the Fields Medal in 2010 "for the proof of conformal invariance of percolation and the planar Ising model in statistical physics." In this talk, I will introduce some of these models including the Ising model, self-avoiding walk, loop-erased random walk, and percolation. I will then discuss SLE, describe some of its basic properties, and touch on the results of Werner and Smirnov as well as some of the major open problems in the area. This talk will be "colloquium style" and is intended for a general mathematics audience.


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