## Research Interests for Xin Zhou

**Research Interests:** *Partial Differential Equations and Integrable Systems*
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**
- McLaughlin, KT-R; Vartanian, AH; Zhou, X,
*Asymptotics of recurrence relation coefficients, hankel determinant ratios, and root products associated with laurent polynomials orthogonal with respect to varying exponential weights*,
Acta Applicandae Mathematicae, vol. 100 no. 1
(2008),
pp. 39-104, ISSN 0167-8019 [doi] [abs]
- with McLaughlin, KT-R; Vartanian, AH; Zhou, X,
*Asymptotics of laurent polynomials of odd degree orthogonal with respect to varying exponential weights*,
Constructive Approximation, vol. 27 no. 2
(2008),
pp. 149-202, ISSN 0176-4276 [doi] [abs]
- Rider, B; Zhou, X,
*Janossy densities for unitary ensembles at the spectral edge*,
International Mathematics Research Notices, vol. 2008 no. 1
(2008), ISSN 1073-7928 [doi] [abs]
- McLaughlin, KT-R; Vartanian, AH; Zhou, X,
*Rational functions with a general distribution of poles on the real line orthogonal with respect to varying exponential weights: I*,
Mathematical Physics, Analysis and Geometry, vol. 11 no. 3-4
(Accepted, 2008),
pp. 187-364, ISSN 1385-0172 [doi] [abs]
- with McLaughlin, KT-R; Vartanian, AH,
*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