Riemann-Hilbert problems, Toeplitz matrices, and applications

March 4 to March 8, 2024

at the

American Institute of Mathematics, Pasadena, California

organized by

Torsten Ehrhardt, Haakan Hedenmalm, Alisa Knizel, and Jani Virtanen

Original Announcement

This workshop will be devoted to soft and classical Riemann-Hilbert problems (RHPs), Toeplitz matrices and determinants, and applications to integrable probability, random matrix theory, and mathematical physics. In particular, Toeplitz matrices and RHPs have been used to treat a variety of problems in these areas—some of the recent advances include the asymptotic study of Toeplitz determinants with piecewise continuous symbols, a genuine asymptotic expansion of the orthogonal polynomials with respect to the exponentially varying weights on the complex plane using soft RHPs, and the asymptotic analysis for the two periodic Aztec diamond using classical RHPs.

The main topics for the workshop are:

  1. asymptotics and double-scaling limits of (block) Toeplitz determinants with Fisher-Hartwig singularities, and their applications;
  2. analysis of soft RHPs beyond the setting of orthogonal polynomial;
  3. interplay between soft RHPs, classical RHPs, and operator theoretic methods;
  4. the study of the asymptotic behavior for various tiling models using RHPs and Toeplitz matrices.

Material from the workshop

A list of participants.

The workshop schedule.

A report on the workshop activities.

A list of open problems.

Workshop videos