# Mathematical Sciences Research Institute

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# Workshop

Quantum Chaos, GUE Conjecture for Zeros of Zeta Functions, Combinatorics, and All That June 07, 1999 - June 11, 1999
 Registration Deadline: June 11, 1999 almost 15 years ago March 07, 1999 about 15 years ago
Parent Program: Random Matrix Models and Their Applications
Organizers Pavel Bleher, D.A. Hejhal, Andrew Odlyzko, and Peter Sarnak
Speaker(s)

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Description

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.

Funding & Logistics

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To apply for funding, you must register by the funding application deadline displayed above.

Students, recent Ph.D.'s, women, and members of underrepresented minorities are particularly encouraged to apply. Funding awards are typically made 6 weeks before the workshop begins. Requests received after the funding deadline are considered only if additional funds become available.

## Show Lodging

MSRI has preferred rates at the Rose Garden Inn, depending on room availability. Reservations may be made by calling 1-800-992-9005 OR directly on their website. Click on Corporate at the bottom of the screen and when prompted enter code MATH (this code is not case sensitive). By using this code a new calendar will appear and will show the MSRI rate on all room types available.

MSRI has preferred rates at the Hotel Durant. Reservations may be made by calling 1-800-238-7268. When making reservations, guests must request the MSRI preferred rate. If you are making your reservations on line, please go to this link and enter the promo/corporate code MSRI123. Our preferred rate is $129 per night for a Deluxe Queen/King, based on availability. MSRI has preferred rates of$149 - $189 plus tax at the Hotel Shattuck Plaza, depending on room availability. Guests can either call the hotel's main line at 510-845-7300 and ask for the MSRI- Mathematical Science Research Inst. discount; or go to www.hotelshattuckplaza.com and click Book Now. Once on the reservation page, click “Promo/Corporate Code“ and input the code: msri. MSRI has preferred rates of$110 - \$140 at the Berkeley Lab Guest House, depending on room availability. Reservations may be made by calling 510-495-8000 or directly on their website. Select “I am an individual traveler affiliated with MSRI”.

Additional lodging options may be found on our short term housing page.