Mathematical Sciences: The Mathematics and Physics of Disordered Materials

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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.