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Tuesday, January 31, 2012

**Abstract:** In this talk I will discuss some recent work of myself in collaboration with Tom Spencer and Arash Fahim. The basic object of study is uniformly elliptic and parabolic PDE in divergence form with random coefficients. It has been known since the 1980's that under suitable scaling the solutions of these equations converge in distribution to the solution of a constant coefficient PDE, the so called homogenized equation. In the talk I shall describe our results on the rate of convergence in homogenization when the random environment is a uniformly elliptic Euclidean Field Theory. The main tools needed to prove these theorems are the Poincare inequality and the Calderon-Zygmund theorem on boundedness in L^p of Fourier multipliers.

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