Research Interests for Xin Zhou

Professor Zhou studies the 1-D, 2-D inverse scattering theory, using the method of Riemann-Hilbert problems. His current research is concentrated in a nonlinear type of microlocal analysis on Riemann-Hilbert problems. Subjects of main interest are integrable and near intergrable PDE, integrable statistical models, orthogonal polynomials and random matrices, monodromy groups and Painleve equations with applications in physics and algebraic geometry. A number of classical and new problems in analysis, numerical analysis, and physics have been solved by zhou or jointly by zhou and his collaborators.

Recent Publications

1. K. T.-R. McLaughlin, A. H. Vartanian, and X. Zhou,, Asymptotics of Orthogonal Laurent Polynomials of even Degree with Respect to Varying Exponential Weights (Preprint, 2008)
2. with K. T.-R. McLaughlin, A. H. Vartanian, Asymptotics of Coefficients of Recurrence Relations, Hankel Determinants Ratios, and Root Products Associated with Orthogonal Laurent Polynomials with Respect to Varying Exponential Weights, journal Acta Applicandae Mathematicae, vol. 100 (2008), pp. 39-104
3. with K. McLaughlin , A.H. Vartanian, Asymptotics of Orthogonal Laurent Polynomials of Odd Degree with Respect to Varying Exponential Weights, Constructive Approximation, vol. 27 (2008), pp. 149-202
4. B. Rider and X. Zhou, Janossy densities for unitary ensembles at the spectral edge, IMRN (Accepted, 2008)
5. K. T.-R. McLaughlin, A. H. Vartanian, and X. Zhou, Rational functions with a general distribution of poles on the real line orthogonal with respect to varying exponential weights, Math. Phys. Anal. Geom. (Accepted, 2008)