Mathematical Sciences: The Mathematics and Physics of Disordered Materials

首席研究员将继续他关于具有无限多个自由度的系统的统计行为的课题的工作。主要的焦点将是均匀无序的系统，如伯努利渗透和自旋玻璃。然而，他也将研究一些涉及统一系统的问题。这些问题将以严格的方法研究，主要植根于概率论，利用重整化群思想和图形（或随机几何）技术。这些学科的范围从纯粹的数学兴趣到一些具有实验分支的学科。这个领域处于数学和物理的交界。

The principal investigator will continue his work on topics concerning the statistical behavior of systems with infinitely many degrees of freedom. The principal focus will be on systems which are homogeneously disordered such as Bernoulli percolation and spin-glasses. However, he will also study some questions involving uniform systems. These problems will be studied with rigorous methods rooted primarily in probability theory, making use of renormalization group ideas and graphical (or stochastic geometrical) techniques. The subjects range from those which are of purely mathematical interest to some which have experimental ramifications. This field is at the interface between mathematics and physics.