Partial Differential Equations and Probability

受不确定性影响的物理系统在整个科学界无处不在。因此，发展一种良好的数学理论来描述和分析这类系统是至关重要的。拟议的程序基于随机均质化的主题，该主题识别受微观、随机效应影响的物理系统的平均、宏观行为。这位被提名者是偏微分方程式和概率论的专家，致力于整合这两个领域的技术，以提供对这一现象的全面理解。

Physical systems subject to uncertainty are ubiquitous throughout the sciences. As a result, it is of fundamental importance to develop a well-posed mathematical theory to describe and analyze such systems. The proposed program is based in the subject of stochastic homogenization, which identifies the average, macroscopic behaviour of a physical system subject to microscopic, random effects. The nominee, a specialist in partial differential equations and probability, is committed to integrating techniques from both fields to provide a comprehensive understanding of this phenomena.