Homogenization theory in random media has been an active research area for the last thirty years and has become a fairly large field at the intersection of applied mathematics, probability theory, and PDEs. Traditionally, it addresses questions of the macroscopic description of solutions of PDEs in random media that do not involve the fine details of small scale variations of the medium. Similar questions arise in numerical computations and are related to uncertainty quantification. Despite much progress in this field, various engineering applications drive the current need to understand regimes where standard homogenization either fails completely or requires rigorous understanding of correctors to homogenization. It is an open challenge in mathematical random media to understand how to go beyond the homogenization regime and to study phenomena that arise outside of its range of validity.
This workshop will bring together experts in various sub-areas of homogenization, such as wave propagation in random media, stochastic averaging, many-particle systems, numerical homogenization, random Hamilton-Jacobi equations, and stochastic partial differential equations. One goal of the workshop is to bring current practical and numerical issues to the attention of mathematicians knowledgeable in random media techniques. Another goal is to address pressing issues beyond homogenization theory. These issues include random media models with slowly decaying correlations or without strong separation of scales. Other important questions to be addressed concern the stochastic stability of solutions and understanding their fluctuations and correctors.