The past decade has seen rapid developments in various areas of mathematics related to the random matrix theory. - First, studies of the properties of Wigner and other ensembles of random matrices using methods of the probability theory. - Second, studies of the properties of orthogonal polynomials, Toeplitz determinants, and Fredholm determinants with universal kernels, by methods of asymptotic analysis with implications for the invariant ensembles of random matrices. - Third, studies of random particle systems appearing in the group representation theory. - Fourth, studies of random walks. - Fifth, applications of random matrices in statistical physics and number theory.

These subjects will form the scope of the week devoted to random matrices. They employ a variety of different methods but deal with not dissimilar objects, therefore we believe that a useful exchange of ideas and creation of new exciting mathematics in the intersection between these subjects is assured.