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Mathematics Colloquium


Date:  Tuesday, December 09, 2008

Title:  From DLA to SLE (and back?)

Abstract:  Diffusion Limited Aggregation (DLA) is a random process of growing sets, proposed by physicists Witten and Sander in 1981, as a model describing the aggregation of randomly moving (diffusing) particles. It is easy to describe and to simulate on a computer, yet very difficult to analyze: Despite intense research by physicists and mathematicians, very little is rigorously known. The Schramm-Loewner Evolution (SLE), discovered by Schramm around 2000, has been instrumental in the resolution of several outstanding conjectures in probability theory, and in providing rigorous proof of numerous predictions from physics. It has generated immense excitement both in the probability and statistical physics community and led to active exchange of ideas. Both have in common that they can be defined by means of compositions of (random) conformal maps. In my talk, aimed at the non-specialist, I will explain and compare the definitions of DLA and SLE, describe some fundamental properties and applications, and will conclude with a discussion of some open questions and speculations.

Speaker:  Steffen Rohde
Institution:  University of Washington


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