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Mathematics Colloquium

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Date:  Tuesday, October 24, 2006

Title:  Harmonic Measure -- An Excursion

Abstract:  Imagine a randomly moving particle beginning in a domain D. The harmonic measure of a set E on the boundary is the probability that this particle hits E before it hits the rest of the boundary. Where is the particle most likely to hit --where does the harmonic measure live? This is one of the most fundamental questions in potential theory. We illustrate this on the von Koch snowflake. Harmonic measure in turn has been a principal tool in geometric function theory. We present examples in entire functions and conformal mappings. Finally, we discuss harmonic measure for a nonlinear equation -- the p-Laplacian, a subject still largely a mystery.


Speaker:  Jang-Mei Wu
Institution:  University of Illinois

 

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