Workshop

This workshop will focus on problems arising in different fields: quantum mechanics, number theory, statistical mechanics, combinatorics, representation theory, and others, which demonstrate surprising universal behavior described by the ensembles of random matrices and random polynomials. The topics of this workshop will include: GUE conjecture for zeros of zeta functions. Mathematical results in the theory of quantum chaos. Poisson conjecture and distribution of values of polynomial forms. Statistical properties of eigenfunctions of integrable and chaotic quantum systems; Universal properties of distribution of eigenvalues and eigenvectors in ensembles of random matrices. Scaling limits, double scaling limits, and their relation to the Painlevé transcendents and their higher generalizations. Correlations between zeros of random polynomials and their application to the problem of universality of the eigenfunction statistics for chaotic quantum systems. Random matrices and noncommutative probability theory; Random matrices in combinatorics and representation theory. Scaling and double scaling limits for the longest increasing subsequence, Young’s diagrams, etc. and their relation to the Painlevé transcendents. The idea of the workshop is to bring together people working in different areas on the problems related to scaling limits and universality and discuss deep hidden connections between these problems.