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Theme Year 1999-2000
Mathematical Physics
L'Astronome dit aussi L'Astrologue. Vermeer de Delft (1632-1675). Louvre © Photo RMN, P. Bernard
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In view of the remarkable advances that are taking place in mathematical physics and of their striking impact
on mathematics and physics, it was decided to devote the 1999-2000 theme activities at the CRM to this area.
The plan is to have a broad coverage with a wide range of activities: an extended program on
quantum integrability, various workshops, mini-courses, etc.
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Table of Contents
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Summer Schools
- IXth CRM Summer School, 1999, at Banff, Alberta,
Theoretical Physics at the End of the XXth Century, June 27 - July 10, 1999
- Séminaire de mathématiques supérieures:
Integrable systems: from classical to quantum,
Department of Mathematics and Statistics (DMS), University of Montréal, July 26 to August 6, 1999.
Organizers:
- Aubert Daigneault (Montréal)
- John Harnad (Concordia and CRM)
- Pavel Winternitz (Montréal and CRM)
Co-sponsors:
- The Fields Institute
- Pacific Institute for Mathematical Sciences (PIms)
- NSERC
- NSF
- DMS
- University of Montréal
Aisenstadt Chair Lecture Series
- Joel Feldman (UBC): August 1999 and April 2000
- Roman Jackiw (MIT): dates to be determined
- Duong H. Phong (Columbia): dates to be determined
Workshops
- Workshop on Theoretical Methods for Strongly Correlated Fermions, May 26-30 1999
- AARMS-CRM Workshop on Bäcklund & Darboux Transformations:
The Geometry of Soliton Theory, June 4-9, 1999
- General relativity, astrophysics and cosmology, June 6-12, 1999
There will be two meetings focussed on topics in gravitational physics.
- Black Holes II: Theory and Mathematical Aspects, June 6-9, 1999
- 8th Canadian Conference on General Relativity and Relativistic Astrophysics, June 10-12, 1999
- Frontiers of Mathematical Physics:
Summer Workshop on Particles, Fields and Strings 99, August 2-20, 1999
- Workshop on Nonlinear Dynamics and Renormalization Group, August 22-27, 1999
- Workshop on Aspects of Quantization, September 23-28, 1999
- Workshop on Quantum Information Processing, December 6-11, 1999
- Workshop on Strings, Duality and Geometry, March 22-25 2000
This one-week workshop, to be held during the month of March 2000, will concentrate on recent
progress in non-perturbative aspects of both field and string theories.
Organizers: Eric D'Hoker (UCLA) and Duong H. Phong (Columbia)
Registration
- Workshop on Isomonodromic Deformations and Applications in Physics, May 1-6, 2000
- Workshop on Mathematical Physicists in Finance and Industry, June 12-17, 2000
Concentration Period
Quantum Integrability 2000
April 2 - June 11, 2000
The CRM will host a semester-long concentration period with several specialists in residence. The
program is organized around two 4-week periods described below and a workshop.
Organizers:
Philippe Di Francesco (North Carolina), André LeClair (Cornell),
Nicolai Reshetikhin (Berkeley), Hubert Saleur (USC)
Mini-courses
Several mini-courses are planned during the year to prepare graduate students for the workshops
and the concentration period.
Orthogonal polynomials and Random Matrices: A Riemann-Hilbert approach
- Lecturer: John Toth (McGill)
- Dates & Times: Fall 1999, Mondays, 11h00-12h30, Burnside Hall, McGill University
- Informal seminar covering (parts of) Percy Deift's book "Orthogonal polynomials and Random Matrices: A Riemann-Hilbert approach", which is available directly from the Courant Institute website (www.courant.edu).
L'intégrabilité des systèmes discrets, avec les applications aux équations de Yang-Baxter
- Lecturer: Claude Viallet (Université Pierre et Marie Curie and CNRS)
« Entropie algébrique (I) » |
Date: | Tuesday November 2 1999 |
Time: | 4:00 pm
| Place: | Centre de recherches mathématiques, Pavillon André-Aisenstadt,
2920, chemin de la Tour
Room 4336
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« Entropie algébrique (II) » |
Date: | Wednesday November 3 1999 |
Time: | 4:00 pm |
Place: | Centre de recherches mathématiques
Room 5340 |
« Lien avec les équations de Yang-Baxter et l¹intégrabilité quantique » |
Date: | Thursday November 11 1999 |
Time | 3:30 pm |
Place: | Centre de recherches mathématiques
Room 5340 |
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Mathematical foundations of second quantization
- Lecturer: Jan Derezinski (Warsaw)
- Dates & Times: January 31, 2000 and Febuary 7, 2000, 10:30 am - 12:30 pm
- Place : CRM, Room 5340
- Various mathematical structures that are used in quantum mechanics and quantum field theory will be described. (Tentative) list of topics:
- Canonical commutation relations.
a) Schrodinger representation;
b) Weyl quantization;
c) Fock spaces, Wick quantization;
d) Metaplectic group;
e) Coherent states;
f) Inequivalent representations;
g) Quasi-free states.
- Canonical anticommutation relations.
- Simple models of quantum field theory.
- Elements of axiomatic quantum field theory.
Isomonodromic deformations and twistor geometry
- Lecturer : Yousuke Ohyama (Osaka & CRM)
- Dates and times : March 27-30, 2000, 3:30 pm
- Place : CRM, Room 4336
Selected Topics in Mathematical Physics: Random Matrices
- Cours ISM Course, Concordia MAST 856K/4
- Lecturer: John Harnad (Concordia & CRM)
- Dates & Times: Winter 2000, Tuesday and Thursday, 10:00 - 11:30 am
- Place : CRM, Room 4336
This course is intended as an introduction to the spectral theory of random matrices. The subject is a remarkable one, with
important applications and connections to a variety of areas of current research; in mathematical physics (statistical theory
of nuclear spectra, topological field theory, quantum gravity, integrable systems), as well as in number theory (distributions of
zeros of zeta functions). The topics to be covered are: the Gaussian ensembles and circular ensembles (Orthogonal,
Symplectic, Unitary); ensembles related to the classical orthogonal polynomials; joint probability densities for eigenvalues;
level densities, partition and correlation functions; level spacing distribution functions; scaling limits in the "bulk" and "edge"
of the spectrum; Fredholm determinant representations, universality; differential equations for correlation functions;
Hamiltonian structure and asymptotics.
Random Schrödinger operators
- Cours ISM Course, McGill MATH 189-708B
- Lecturer: Vojkan Jaksic (Ottawa)
- Dates & Times: Winter 2000, Thursday, 1:00 - 3:00 pm
- Place : CRM, Room 5340
Organizing Committee
- Philippe Di Francesco (North Carolina)
- Lisa Jeffrey (Toronto)
- André LeClair (Cornell)
- Yvan Saint-Aubin (Montréal, CRM)
- Luc Vinet (McGill, CRM)
Further Information
Those wishing to participate in the above activities are invited to write to:
Louis Pelletier
Centre de recherches mathématiques (CRM)
Université de Montréal
C.P. 6128, Succ. centre-ville
Montréal (Québec) CANADA H3C 3J7
E-mail: ACTIVITES@CRM.UMontreal.CA
World Wide Web: http://www.CRM.UMontreal.CA/mathphys
FAX: (514) 343-2254
Telephone: (514) 343-2197
4 February 2000, webmaster@CRM.UMontreal.CA