# Xin Zhou

- Professor Emeritus of Mathematics

**External address:**PO Box 90320, Durham, NC 27708

**Internal office address:**Box 90320, Durham, NC 27708-0320

**Phone:**(919) 660-2800

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.

### Selected Grants

Riemann-Hilbert Problem and Integrable Systems awarded by National Science Foundation (Principal Investigator). 2006 to 2010

Riemann-Hilbert problem and integrable systems awarded by National Science Foundation (Principal Investigator). 2003 to 2007

Inverse Scattering Theory awarded by National Science Foundation (Principal Investigator). 2000 to 2003

(97-0380) Inverse Scattering Theory awarded by National Science Foundation (Principal Investigator). 1997 to 2000

(94-0255) Inverse Scattering Theory awarded by National Science Foundation (Principal Investigator). 1994 to 1997

Rider, B., and X. Zhou. “Janossy densities for unitary ensembles at the spectral edge.” *International Mathematics Research Notices*, vol. 2008, no. 1, Dec. 2008. *Scopus*, doi:10.1093/imrn/rnn037.
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McLaughlin, K. T. R., et al. “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, Nov. 2008, pp. 187–364. *Scopus*, doi:10.1007/s11040-008-9042-y.
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McLaughlin, K. T. R., et al. “Asymptotics of laurent polynomials of odd degree orthogonal with respect to varying exponential weights.” *Constructive Approximation*, vol. 27, no. 2, Mar. 2008, pp. 149–202. *Scopus*, doi:10.1007/s00365-007-0675-z.
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McLaughlin, K. T. R., et al. “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, Jan. 2008, pp. 39–104. *Scopus*, doi:10.1007/s10440-007-9176-0.
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McLaughlin, K. T. .. R., and 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.

Tovbis, A., et al. “Semiclassical focusing nonlinear schrödinger equation i: Inverse scattering map and its evolution for radiative initial data.” *International Mathematics Research Notices*, vol. 2007, Dec. 2007. *Scopus*, doi:10.1093/imrn/rnm094.
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Deift, P., et al. “The Widom-Dyson constant for the gap probability in random matrix theory.” *Journal of Computational and Applied Mathematics*, vol. 202, no. 1 SPECIAL ISSUE, May 2007, pp. 26–47. *Scopus*, doi:10.1016/j.cam.2005.12.040.
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McLaughlin, K. T. R., et al. “Asymptotics of Laurent polynomials of even degree orthogonal with respect to varying exponential weights.” *International Mathematics Research Papers*, vol. 2006, Oct. 2006. *Scopus*, doi:10.1155/IMRP/2006/62815.
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Tovbis, A., et al. “On the long-time limit of semiclassical (zero dispersion limit) solutions of the focusing nonlinear Schrödinger equation: Pure radiation case.” *Communications on Pure and Applied Mathematics*, vol. 59, no. 10, Jan. 2006, pp. 1379–432. *Scopus*, doi:10.1002/cpa.20142.
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Deift, P., et al. “The Widpm-Dyson constant for the gap probability in random matrix theory.” *A Special Edition of the Journal of Computational and Applied Mathematics*, 2006.