Transport and localization in random media: theory and applications

Homogenization and regularity for nonlinear elliptic equations

Scott Armstrong

New York University

I will give an overview of some recent quantitative results for linear elliptic PDEs with random coefficients, with particular focus on the role played by the "large-scale" regularity theory. I will then describe the challenges in extending the methods to nonlinear equations and some recent partial results in this direction.