Mathematical Physics Laboratory

isomonodromiques et problèmes de Riemann-Hilbert

Working Seminar on Random Matrices, Isomonodromic Deformations and Riemann-Hilbert Problems

Concordia University

Library Building, 1400 de Maisonneuve Blvd. West

LB 921-04 (Ninth floor meeting room)

Title/titre: "The inverse spectral problem for arbitrary rational Lax matrices"

Speaker/Conférencier: Marco Bertola (Concordia and CRM)

We provide an extension of the old Baker-Akhiezer approach in order to give explicit formulae for the entries of an arbitrary rational Lax matrix knowing certain spectral data.

Title/titre: "Determinants of Laplacians, moduli spaces of Riemann surfaces and Abelian differential"

Speaker/Conférencier: Alexey Kokotov (Concordia)

We generalize the well-known Ray-Singer formula for the determinant of the Laplacian on elliptic surfaces to the case of compact Riemann surfaces of higher genus. To illustrate the potential applications of this result we study the determinant of the Laplacian as a Morse function on the moduli space of Riemann surfaces of genus two. Its stationary points are identified as surfaces with large groups of automorphisms. As a corollary we calculate the orbifold Euler characteristics of the moduli space and its symmetric strata.

Title/titre: "Remarks on complex geometry of 3-monopole"

Speaker/Conférencier: Victor Enolski (CRM, Concordia)

Title/titre: "Effective integration of the Nonlinear Vector Schrödinger Equation"

Speaker/Conférencier: Victor Enolski (CRM, Concordia)

(Based on collaborative work with A.Its and J.Elgin.)

Title/titre: "Isomonodromic equations satisfied by biorthogonal polynomials, integral representations and duality"

Speaker/Conférencier: John Harnad (CRM, Concordia)

(Based on collaborative work with M. Bertola and A.Its.)

Title/titre: What is a Dynamical R-Matrix?

Speaker/Conférencier: Prof Axel Winterhalder (Universidade Estadual do Maranhao, Brazil)

Title/titre: The inverse asympto-monodromic method: asymptotics of orthogonal polynomials via Strebel, Stokes, Deift--Zhou and Its (Part I.)

Speaker/Conférencier: Marco Bertola

(Concordia and CRM)

Title/titre: The inverse asympto-monodromic method, part II: Boutroux admissible curves and Stokes--Kirchoff differentials

Speaker/Conférencier: Marco Bertola

(Concordia and CRM)

Title/titre: The inverse asympto-monodromic method, part III: Boutroux admissible curves and Stokes--Kirchoff differentials

Speaker/Conférencier: Man Yue Mo (CRM)

Title/titre: The inverse asympto-monodromic method, part IV: reconstruction of arbitrary admissible Boutroux curves from a forest of decorated trivalent loop-free trees using Strebel weldings

Speaker/Conférencier: Marco Bertola (Concordia and CRM)

Title/titre: Determinant of Laplacians and Schottky groups

Speaker/Conférencier: Andrew McIntyre (Concordia and CRM)

1. Schiffer and Bergman kernels; Zograf's product formula

2. Generalization of Riemann normalization of abelian differentials to higher
order differentials

3. Variational formula for det laplacian on higher order differentials in
"fermionic" form

Item 2 is self-contained and may be of independent interest.

Title/titre: On the connection of free fermions and integrable hierarchies: the case for quantum dynamics

Speaker/Conférencier: Paul Wiegmann, James Frank Institute, Enrico Fermi Institute, Univ. of Chicago

Title/titre: Schur functions expansions of algebro-geometric tau functions

Speakers/Conférenciers: Viktor Enolskii (Kiev, CRM and Concordia) and John Harnad (Concordia and CRM)

Part I. (J.H.) The Segal-Wilson Grassmannian, determinantal line bundles and Schur function expansions in general

Part II. (V.E.) The Schur function expansion for tau functions of genus g=1 (Weierstrass), 2 (Baker) and, for trigonal curves of g=3 (Enolskii et al)

Working seminar on random matrices, isomonodromic deformations and iemann-Hilbert Problems: Fall 2005

For further information: *bertola@CRM.UMontreal.CA*