Home /  Random Matrices, Statistical Mechanics, and Integrable Systems


Random Matrices, Statistical Mechanics, and Integrable Systems February 22, 1999 - February 26, 1999
Registration Deadline: February 26, 1999 over 25 years ago
To apply for Funding you must register by: November 22, 1998 over 25 years ago
Parent Program:
Organizers B. Dubrovin, A. Its, M. Mehta (Chair), and N. Reshetikhin

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This workshop will focus on the relations of random matrices to integrable systems and to exactly solvable statistical mechanics and topological field models. The following three groups of topics will be of primary interest: Random matrices, orthogonal polynomials, and integrable systems of differential equations of the Painlevé and KP types. The Riemann-Hilbert and Isomonodromy approachies and their relations to semiclassical analysis. The vertex operators and Virasoro algebra techniques. Correlation functions of exactly solvable quantum field and statistical mechanics models. The quantum Calogero-Sutherland and Calogero-Moser systems and the Knishnik-Zamolodchikov equation. XXX and XXZ models and the quantum Knishnik-Zamolodchikov equation. Relations to the q-special functions and to the representation theory of quantum affine algebras. Matrix integrals and topology of the moduli spaces of algebraic curves. Relations to topological field theories. Frobenius manifolds, Painlevé transcendents, and isomonodromy deformations. The indicated directions share several common analytic and algebraic features, e.g. Riemann-Hilbert problem, integrable Fredholm operators, Virasoro algebra, KP and Toda hierarchies, etc. One of the principal objectives of the workshop is to discuss extensively these remarkable similarities and hence to advance in understanding of the basic mathematical structures that lie behind them.
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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Feb 22, 1999
08:00 AM - 05:00 PM
  Boundary conformal field theory and representation of the fusion algebra
Jean-Bernard Zuber
08:00 AM - 05:00 PM
  D-particle bound states and generalized instantons
Samson Shatashvili
08:00 AM - 05:00 PM
  Ageneralized Darboux-Halphen system, 2
Sarbarish Chakravarty
08:00 AM - 05:00 PM
  Integrable Structures Inherent in Random Matrix Theory
Mark Adler
08:00 AM - 05:00 PM
  Quantum Resurgence
Eric Delabaere
08:00 AM - 05:00 PM
  On the relationship between the discreet and continuous Painleve equations
Peter Clarkson
08:00 AM - 05:00 PM
  On the semi-classical limit of the focusing nonlinear Schroedinger equation
Ken McLaughlin
08:00 AM - 05:00 PM
  Some unsolved problems in the Random MAtrices and Hamiltonians
Anthony Zee
08:00 AM - 05:00 PM
  Universality and Scaling for Zeros of Random Polynomials
Paul Bleher
08:00 AM - 05:00 PM
  Locus Configurations in the Theory of Calogero-Moser systems and WDVV equations
Alexander Veselov
08:00 AM - 05:00 PM
  Baxter's Q-operator and the Virasoro algebra
Edward Frenkel
08:00 AM - 05:00 PM
  Extended Vertex operator algebras and monomial bases
Tetsuji Miwa
08:00 AM - 05:00 PM
  Discriminants, q-Differences and Electrostatics
Mourad Ismail
08:00 AM - 05:00 PM
  Behavior of a Quantum Fluid Interacting by an Inverse-square Potential in a Time-dependent Harmonic Trap
Bill Sutherland
08:00 AM - 05:00 PM
  Operators on Graphs and Symplectic Geometry
Sergei Novikov
08:00 AM - 05:00 PM
  The operator-valued RHP for the correlation functions of the Quantum NLS
Nikita Slavnov
08:00 AM - 05:00 PM
  Algebra of Integral Operators and Correlation functions of 1D electron gas
Vladimir Korepin
08:00 AM - 05:00 PM
  Correlation Functions of XXZ model at finite temperature
Barry McCoy
08:00 AM - 05:00 PM
  Chiral Potts Model
Rodney Baxter
08:00 AM - 05:00 PM
  Asymptotics for random permutations
Percy Deift
08:00 AM - 05:00 PM
  What is HAAR Measure Anyways?
Persi Diaconis (Stanford University)
08:00 AM - 05:00 PM
  Fay Identities, Fredholm determinants, soliton formulas and random matrices
Takahiro Shiota
08:00 AM - 05:00 PM
  Phase Transitions and Random Matrices
Giovanni Cicuta
08:00 AM - 05:00 PM
  Scaling limit of random matrices and KdV flow
Eduoard Brezin