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Program

Random Matrix Theory, Interacting Particle Systems and Integrable Systems August 16, 2010 to December 17, 2010

Organizers Jinho Baik (University of Michigan), Alexei Borodin (California Institute of Technology), Percy A. Deift* (New York University, Courant Institute), Alice Guionnet (École Normale Supérieure de Lyon, France), Craig A. Tracy (University of California, Davis), and Pierre van Moerbeke, (Université Catholique de Louvain, Belgium)

Description RMT has emerged as a model for an extraordinary variety of problems in mathematics, physics and engineering. Applications run the gamut from the scattering of neutrons in nuclear physics, to the distribution of the zeros of the Riemann zeta function on the critical line, and include:

• combinatorics
• the representation theory of large groups
• multivariate statistics
• numerical analysis and the estimation problem for condition numbers of random
• linear systems
• tiling problems
• enumerative topology
• Painleve theory
• interacting particle systems
• transportation problems
• random growth processes
• quantum transport problems
• wireless communications

amongst many others. RMT is now well-recognized in the mathematics, physics, engineering communities. The Tracy-Widom distributions for the largest eigenvalue of a random matrix are entering the standard toolkit of the probabilist.

In addition to show-casing the above applications, the Program will also focus on internal questions in RMT, such as universality for eigenvalue distributions of invariant ensembles, as well as the more recent work on Wigner ensembles. The role of asymptotic methods from the theory of integrable systems, such as the steepest descent method for Riemann-Hilbert problems, will also be highlighted.

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