Mathematical Sciences Research Institute

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Random Matrices, Statistical Mechanics, and Integrable Systems February 22, 1999 - February 26, 1999
Registration Deadline: February 26, 1999 about 24 years ago
To apply for Funding you must register by: November 22, 1998 over 24 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 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.

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MSRI does not hire an outside company to make hotel reservations for our workshop participants, or share the names and email addresses of our participants with an outside party. If you are contacted by a business that claims to represent MSRI and offers to book a hotel room for you, it is likely a scam. Please do not accept their services.

MSRI has preferred rates at the Hotel Shattuck Plaza, depending on room availability. Guests can call the hotel's main line at 510-845-7300 and ask for the MSRI- Mathematical Science Research Institute discount. To book online visit this page (the MSRI rate will automatically be applied).

MSRI has preferred rates at the Graduate Berkeley, depending on room availability. Reservations may be made by calling 510-845-8981. When making reservations, guests must request the MSRI preferred rate. Enter in the Promo Code MSRI123 (this code is not case sensitive).

MSRI has preferred rates 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 "Affiliated with the Space Sciences Lab, Lawrence Hall of Science or MSRI." When prompted for your UC Contact/Host, please list Chris Marshall (coord@msri.org).

MSRI has a preferred rates at Easton Hall and Gibbs Hall, depending on room availability. Guests can call the Reservations line at 510-204-0732 and ask for the MSRI- Mathematical Science Research Inst. rate. To book online visit this page, select "Request a Reservation" choose the dates you would like to stay and enter the code MSRI (this code is not case sensitive).

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

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Schedule, Notes/Handouts & Videos
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Feb 22, 1999
08:00 AM - 05:00 PM
  Discriminants, q-Differences and Electrostatics
Mourad Ismail
08:00 AM - 05:00 PM
  Scaling limit of random matrices and KdV flow
Eduoard Brezin
08:00 AM - 05:00 PM
  Phase Transitions and Random Matrices
Giovanni Cicuta
08:00 AM - 05:00 PM
  Fay Identities, Fredholm determinants, soliton formulas and random matrices
Takahiro Shiota
08:00 AM - 05:00 PM
  What is HAAR Measure Anyways?
Persi Diaconis (Stanford University)
08:00 AM - 05:00 PM
  Asymptotics for random permutations
Percy Deift
08:00 AM - 05:00 PM
  Chiral Potts Model
Rodney Baxter
08:00 AM - 05:00 PM
  Correlation Functions of XXZ model at finite temperature
Barry McCoy
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
  The operator-valued RHP for the correlation functions of the Quantum NLS
Nikita Slavnov
08:00 AM - 05:00 PM
  Operators on Graphs and Symplectic Geometry
Sergei Novikov
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
  Boundary conformal field theory and representation of the fusion algebra
Jean-Bernard Zuber
08:00 AM - 05:00 PM
  Extended Vertex operator algebras and monomial bases
Tetsuji Miwa
08:00 AM - 05:00 PM
  Baxter's Q-operator and the Virasoro algebra
Edward Frenkel
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
  Universality and Scaling for Zeros of Random Polynomials
Paul Bleher
08:00 AM - 05:00 PM
  Some unsolved problems in the Random MAtrices and Hamiltonians
Anthony Zee
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
  On the relationship between the discreet and continuous Painleve equations
Peter Clarkson
08:00 AM - 05:00 PM
  Quantum Resurgence
Eric Delabaere
08:00 AM - 05:00 PM
  Integrable Structures Inherent in Random Matrix Theory
Mark Adler
08:00 AM - 05:00 PM
  Ageneralized Darboux-Halphen system, 2
Sarbarish Chakravarty
08:00 AM - 05:00 PM
  D-particle bound states and generalized instantons
Samson Shatashvili