Pavel Bleher, IUPUI, Indianapolis:Riemann--Hilbert approach to the six-vertex model

Abstract. We will discuss the Riemann--Hilbert approach to the exact solution
of the six-vertex model with domain wall boundary conditions in different phase regions.
The exact solution includes several steps:

  * The Yang--Baxter equations and the Izergin--Korepin formula.
  * The Zinn-Justin matrix integrals and associated orthogonal polynomials.
  * The Riemann-Hilbert approach and the Deift--Zhou nonlinear steepest descent method for continuous and discrete orthogonal polynomials.
  *  The asymptotic analysis of the partition function of matrix models.

We will review the main steps and results concerning the exact solution. The talk will be self-contained and no prerequisites will be required.