Scott Armstrong (NYU)

Title: Quantitative results in stochastic homogenization

I will give an overview of some recent progress in elliptic homogenization with random coefficients with a focus on the precise scaling of the correctors. In the first lecture I will introduce the model, give some connections to problems in probability theory and try to give a feeling for some of the mathematical difficulties encountered in analyzing it.

In the second lecture I will give an outline of a "bootstrap" or "renormalization" scheme (developed jointly with Kuusi and Mourrat) for obtaining an optimal quantitative understanding of the correctors, emphasizing the important role played by the higher regularity theory in homogenization (based on previous joint work with Smart).