mardi 9 janvier 2001:16h00 Conférencier / Lecturer: Jorgen Rasmussen, Univ. of Lethbridge
Titre / Title: su(N) tensor product multiplicities and virtual Berenstein-Zelevinsky triangles.
mardi 9 janvier 2001:16h00
Conférencier / Lecturer:
Jorgen Rasmussen, Univ. of Lethbridge
Titre / Title: su(N) tensor product multiplicities and virtual Berenstein-Zelevinsky
triangles.
mardi 23 janvier 2001: 16h00
Conférencier / Lecturer:
Luc Frappat, CNRS, LAPP
Titre / Title: Elliptic algebras, q-deformed W-algebras and Yangian limits.
mardi 30 janvier 2001: 16h00
Conférencier / Lecturer:
Bertrand Eynard, SPHT Saclay (France)
Titre / Title: Random matrices and (skew)-orthogonal polynomials
Resume: Many physical systems can be represented by a random matrixm,
and they share some universal properties, The method of Orthogonal Polynomials
was invented in order to understand universlity in random matrices *skew-orthogonal
poynomials for non-hermitian matrices). I will briefly introduce the subject
and show how one can derive some asymptotics for the skew-orthogonal polynomials.
mardi 6 février 2001: 16h00
Conférencier / Lecturer: J. Harnad, CRM & Université Concordia
Titre/Title: Multi-Hamiltonian
structures, R-matrices and spectral separation of variables, I
Resume: A connection
is made between: separation of variables in the spectral Darboux coordinates
naturally associated to isospectral Lax matrix flows on finite dimensional Poisson
subspaces of loop algebras in the rational R-matrix setting and: separation
of variables in the "Nijenhuis coordinates" associated with multi-Hamiltonian
systems. This is extended to multi-Hamiltonian structures related to trigonometric
and elliptic R-matrices, and to the quadratic (Sklyanin) brackets on loop groups,
viewed as Poisson Lie groups.
mardi 13 février 2001: 16h00
Conférencier / Lecturer: Bertrand Eynard, SPHT Saclay (France)
Titre / Title: O(n) Random matrix models.
Resume: The O(n) model is a famous toy model for 2D statistical physics.
When put on a random lattice, the O(n) model is coupled to gravity, and the
partition function can be represented by a matrix integral. The large n limit
of that integral can be computed, and the results involve elliptic functions
even in the one cut-case (because there is another "ghost" cut). The O(n) model
is very rich because it interpolates all the possible (p,q) conformal minimal
models, as well as non-rational cases.
mardi 20 février 2001: 16h00
Conférencier / Lecturer: Jacques Hurtubise, CRM & Univ. McGill
Titre / Title: Multi-Hamiltonian structures, R-matrices and spectral
separation of variables, II
mardi 27 février 2001: 16h00
Conférencier / Lecturer: Oksana Yermolayeva, CRM & Concordia
Titre / Title: A review of the f-g method in orthogonal polynomials.
mardi 6 mars 2001: 16h00
| ANNULÉ |
Conférencier / Lecturer: Oleg Bogoyavlenski, Queens University,
Kingston
Titre/Title: Infinite dimensional Lie group of symmetries of equations
of physical significance
Resume: An infinite dimensional Lie group $G$ of symmetries of the magnetohydrodynamics
equilibrium equations is introduced that generates continuous families of new
equilibrium solutions from any known ones. The Lie group $G$ depends upon the
topology of the magnetic surfaces for a given equilibrium and is parametrized
by arbitrary smooth functions on the corresponding graph $\Gamma$.
mardi, le 13 mars: 16h00
Conférencier / Lecturer : A. Zhedanov (Univ. Donetsk, CRM)
Titre/Title: "Integrable chains, algorithms and orthogonality I. & II"
Resume/abstract: We describe relations between Darboux transformations,
numeric algorithms in linear algebra, integrable systems like Toda and relativistic
Toda chains, and orthogonality properties of corresponding eigenfunctions. In
particular, we present a new class of rational functions which are biorthogonal
on elliptic grids.
mardi, le 20 mars: 16h00
Conférencier / Lecturer : A. Zhedanov (Univ. Donetsk, CRM)
Titre/Title: "Integrable chains, algorithms and orthogonality I. & II"
Resume/abstract:
We describe relations between Darboux transformations, numeric algorithms in
linear algebra, integrable systems like Toda and relativistic Toda chains, and
orthogonality properties of corresponding eigenfunctions. In particular, we
present a new class of rational functions which are biorthogonal on elliptic
grids.
jeudi, le 22 mars: 15h30 (session supplémentaire)
Conférencier C. Klein, Institut für Theoretische Physik Eberhard-Karls-Universität,
Tübingen
Titre/Title : Relativistic dust disks and hyperelliptic Riemann surfaces
Resume: Infinitesimally thin disks of pressureless matter, so called
dust, are discussed in astrophysics as models for certain galaxies and the matter
in accretion disks around black holes. Since the vacuum Einstein equations in
the stationary axisymmetric case are equivalent to the completely integrable
Ernst equation, global spacetimes can be constructed for these models. The matter
in the disk leads to a boundary value problem for the Ernst equation which can
be treated with Riemann-Hilbert techniques. In the scalar case this leads to
the Poisson integral. The matrix Riemann-Hilbert problem can be gauge transformed
to a scalar problem on a Riemann surface. In the case of rational jump data,
this surface is compact and the corresponding solutions to the Ernst equation
form a subclass of Korotkin's hyperelliptic solutions. Within this class one
can study which boundary value problems can be solved on a given Riemann surface.
As an example we discuss a family of disks made up of two counterrotating dust
components. The complete metric is given explicitly in terms of hyperelliptic
functions which are evaluated numerically.
mardi, le 27 mars :
16h00
Conférencier / Lecturer : P Bracken (CRM)
Titre/Title : Symmetries, Integrability and MultiSoliton Solutions of
the Generalized Weierstrass System.
Resume/Abstract:
The Generalized Weierstrass system
for inducing minimal surfaces in R^3 as proposed by B Konopelchenko will be
introduced. The integrability of the system has been studied, in particular,
by using a specific transformation, the initial system can be transformed into
the completely integrable two-dimensional Euclidean nonlinear sigma model. The
group invariant solutions of the sigma model system have been classified, and
we briefly outline how this is done. Of more interest is that these results
lead to very complicated new multisoliton solutions. It is shown how conditional
symmetries lead to an Auto-Backlund for the system, from which the Theorem of
Permutability can be formulated. Finally, we outline how this work can be extended
to surfaces immersed in R^4, and give some new multisoliton solutions, and discuss
a class of vortex solution.
mardi, le 3 avril : 16h00
ATTENTION! Lieu: (exceptionellement) Concordia Library Building LB 450 (1400
de Maisonneuve O.)
Conférencier/Speaker: Chongying Dong, University of California,
Santa Cruz
Titre / Title: Monster, Moonshine and Vertex (Operator) Algebras
Resume / Abstract: The Monster is the largest sporadic finite simple
group. Moonshine is the relationship between the monster and modular functions.
Vertex operator algebras are a new class of algebraic structures which have
recently arisen in mathematics and physics. In this talk we will review the
Mckay-Thompson-Conway-Norton moonshine conjecture and discuss how Borcherds
proved the conjecture for the Frenkel-Lepowsky-Meurman's moonshine vertex operator
algebra by using the monster Lie algebra. We will also present recent developments
in orbifold conformal field theory and Norton's generalized Moonshine conjecture.
mardi, le 10 avril : 16h00
Conférencier/Speaker: Dmitri Korotkin (Univ. Concordia, CRM)
Titre/Title: Isomonodromic deformations and Hurwitz spaces: tau-function
and determinant of Laplacian operator
Resume: We discuss a class of isomonodromic deformations associated to
Hurwitz spaces. A solution of the associated Riemann-Hilbert problem is given
in terms of a Szego reproducing kernel. Calculation of isomonodromic tau-function
of Jimbo, Miwa et al reveals a close link with the determinant of the Laplacian
and Cauchy-Riemann operators.
mardi, le 17 avril : 16h00
Conférencier/Speaker : Dmitri Korotkin (Univ. Concordia, CRM)
Titre/Title: Isomonodromic deformations and Hurwitz spaces: tau-function
and determinant of Laplacian operator II.
Resume / Abstract: We discuss a class of isomonodromic deformations associated
to Hurwitz spaces. A solution of the associated Riemann-Hilbert problem is given
in terms of a Szego reproducing kernel. Calculation of isomonodromic tau-function
of Jimbo, Miwa et al reveals a close link with the determinant of the Laplacian
and Cauchy-Riemann operators.
mardi, le 24 avril : 16h00
Conférencier/Speaker: Anna Krasowska (Univ. Concordia)
Titre/Title: Wigner functions for semidirect product groups R^n \rtimes
H
Resume / Abstract: In this talk we consider semidirect product groups
R^n \rtimes H admitting open free H-orbits in \hat R^n (dual to R^n). We give
a classification of such groups in dim n=3. Their square -integrable representations
give a basis for a construction of general Wigner functions, a useful tool in
signal analysis and quantum optics. We also discuss the relation between wavelets
and Wigner functions.
mardi, le 1er mai : 16h00
Conferencier/Speaker: Marco
Bertola (CRM, Univ. Concordia)
Titre/Title: Duality in Random Matrices and Biorthogonal Polynomials
Resume/Abstract : Correlation functions and spacing distributions in
two-matrix models may be computed as determinants involving "integrable" Fredholm
kernels. These may be expressed in the case of 2-matrix models by a generalized
Darboux-Christoffel fomula consisting of finite sums over biorthogonal sequences
of quasi-polynomials and their Fourier-Laplace transforms. These in turn give
rise to representations of the Heisenberg commutation relations for the shift
operators which in the case of measures that are exponentials of polynomials,
are finite band semi-infinite matrices of band sizes equal to the degrees of
the polynomials defining the measure. These representations may be "folded"
and used to determine "dual pairs" of covariant derivative operators involving
matrices having the size of the band in one of the shift operators, with entries
that are polynomials of degree equal to the size of the band of the dual operator.
Interchanging the two, it is shown that the resulting characteristic polynomials
are identical. Deforming the measure within this class gives rise to commuting
flows that preserve the monodromies of both the operators.