Riemann-Hilbert problems, Toeplitz matrices, and applications

Riemann-Hilbert problems, Toeplitz matrices, and applications

This workshop, sponsored by AIM and the NSF, 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.

This event will be run as an AIM-style workshop. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and parallel working sessions.

The deadline to apply for support to participate in this workshop has passed.

For more information email workshops@aimath.org

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