Home /  Quantum Chaos, GUE Conjecture for Zeros of Zeta Functions, Combinatorics, and All That


Quantum Chaos, GUE Conjecture for Zeros of Zeta Functions, Combinatorics, and All That June 07, 1999 - June 11, 1999
Registration Deadline: June 11, 1999 about 25 years ago
To apply for Funding you must register by: March 07, 1999 over 25 years ago
Parent Program:
Organizers Pavel Bleher, D.A. Hejhal, Andrew Odlyzko, and Peter Sarnak

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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.
Keywords and Mathematics Subject Classification (MSC)
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
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To apply for funding, you must register by the funding application deadline displayed above.

Students, recent PhDs, 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.

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For information about recommended hotels for visits of under 30 days, visit Short-Term Housing. Questions? Contact coord@slmath.org.

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Schedule, Notes/Handouts & Videos
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Jun 07, 1999
08:00 AM - 05:00 PM
  Spanning sets for automorphic forms and dynamics of the frame flow on complex hyperbolic spaces
Svetlana Katok
08:00 AM - 05:00 PM
  Spectra of Elements in Group rings and Random Matrix Theory
Alex Gamburd
08:00 AM - 05:00 PM
  Random Polynomials in Quantum Chaos: a Review
Patricio Leboeuf
08:00 AM - 05:00 PM
  Zeros of Quadratic L-funcions close to the Real Axis
Ali Ozluk
08:00 AM - 05:00 PM
  Linear combinations of L-functions and Zeros on the Critical Line
Atle Selberg
08:00 AM - 05:00 PM
  Linear combinations of L-functions and Zeros off the Critical Line
Dennis Hejhal
08:00 AM - 05:00 PM
  Complements to Li's Criterion for the Riemann Hypothesis
Jeff Lagarias
08:00 AM - 05:00 PM
  Artin L-functions of Graph Coverings
Audrey Terras
08:00 AM - 05:00 PM
  Beyond Pair Corelation
Kannan Soundararajan
08:00 AM - 05:00 PM
  The Second moment of the reciprocal of the Riemann zeta functin and it's derivative
Steven Gonek
08:00 AM - 05:00 PM
  The quantized cat map and quantum ergodicity
Zeev Rudnick
08:00 AM - 05:00 PM
  The Logarithmic Derivative of the Riemann Zeta-Function and Pair Correlation of Zeros
Daniel Goldston
08:00 AM - 05:00 PM
  Mean Values of L-functions and symmetry
David Farmer
08:00 AM - 05:00 PM
  Coloring Random Triangulations
Philippe DiFrancesco
08:00 AM - 05:00 PM
  Discrete orthogonal polynomials ensembles
Kurt Johansson
08:00 AM - 05:00 PM
  The Asymptotics of Monotone of subsequences of involutions
Jinho Baik
08:00 AM - 05:00 PM
  Z-Measures on the partitions, Robinson-Schensted-Knuth correspondence
Alexei Borodin
08:00 AM - 05:00 PM
  On the distribution of the total energy of a system of non-interacting fermions
Oriel Bohigas
08:00 AM - 05:00 PM
Jon Keating
08:00 AM - 05:00 PM
  Zeros of L-functions: computations and the behavior of low zeros
Michael Rubinstein
08:00 AM - 05:00 PM
  Random matrix theory and zeroes of zeta functions - a survey
Peter Sarnak
08:00 AM - 05:00 PM
  Correlations in Chaotic Eigenfunctions in Space and Time
Mark Srednicki
08:00 AM - 05:00 PM
  Matrix Models, Links and Knots
Paul Zinn-Justin
08:00 AM - 05:00 PM
  Spectral Statistics
Eugene Bogomolny
08:00 AM - 05:00 PM
  Exact Quantization method for General 1D polynomials potentials
Andre Voros
08:00 AM - 05:00 PM
  Universality and Scaling of correlations of Zeros and complex manifolds
Steve Zelditch
08:00 AM - 05:00 PM
  On Universality of the Smoothes Eigenvalue density of large random matrices
Alexei Khorunzhy
08:00 AM - 05:00 PM
  Random Matrix with deterministic source
Shinobu Hikami
08:00 AM - 05:00 PM
  Double Scaling Limit for Orthogonal Polynomials
Pavel Bleher
08:00 AM - 05:00 PM
  Dual Pairs in Random Matrix Theory
Martin Zirnbauer
08:00 AM - 05:00 PM
  Algebraic Study of the Pair correlation function for quantum maps
Stephane Nonnenmacher
08:00 AM - 05:00 PM
  Deformed Random Matrix ensembles and Anderson Hamiltonian
Shinsuke Nishigaki
08:00 AM - 05:00 PM
  Universality of unitary ensembles in the microscopic scaling limit
Gernot Akemann