Momar Dieng

Contact information

Momar Dieng
Department of Mathematics
The University of Arizona
617 N. Santa Rita Avenue
P.O. Box 210089
Tucson, AZ 85721-0089
USA
Tel: (520) 621-6892
Fax: (520) 621-8322
Office: MATH 305

I am a postdoctoral fellow in the Department of Mathematics at the University of Arizona. My mathematical interests are diverse but my current work spans the areas of integrable systems theory, nonlinear partial differential equations, random matrix theory, and their interrelationship.

On the integrable systems theory side, my work with Professor Kenneth McLaughlin involves the semi-classical analysis of the focusing nonlinear Schrödinger equation. A good portion of the mathematics involved falls into what is generally described as "integrable systems theory." It includes a careful analysis of the direct spectral problem (the Zakharov-Shabat ode system), as well as attacking the inverse spectral problem via Riemann-Hilbert, and d-bar techniques.

My Ph.D. thesis was written in the area of random matrix theory (RMT), under the supervision of Professor Craig A. Tracy. RMT is a vibrant area of research at the intersection of probability theory and statistics, operator theory, combinatorics, number theory, integrable systems, quantum chaos to name only a few of a growing list of related areas within mathematics. The main object of study in RMT is the statistical behavior of eigenvalues in certain probability spaces of matrices. Asymptotic analysis via Riemann-Hilbert problems provides a powerful approach to important questions in RMT, and is an example of the growing and productive interaction between integrable systems and RMT. I am interested in exploring more applications of Riemann-Hilbert techniques, as well as other integrable systems theory techniques, in RMT.

You can find out more about my work in these areas here.