Stochastic homogenization: renormalization, regularity, and quantitative estimates

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Scott Armstrong, Courant Institute of Mathematical Sciences, New York University
Fine Hall 314

There has been a lot of work in recent years on the problem of understanding the behavior of solutions of PDEs with random coefficients, with most of the work focused on linear elliptic equations in divergence form. I will give an overview of recent joint works with Smart, Kuusi and Mourrat in which we introduce a renormalization group" method, which leads to a very precise, quantitative description of the solutions.