Xin Zhou | Scholars@Duke

Xin Zhou
Professor Emeritus of Mathematics

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.

Current Appointments & Affiliations

Professor Emeritus of Mathematics, Mathematics, Trinity College of Arts & Sciences 2014

Contact Information

Box 90320, Durham, NC 27708-0320
PO Box 90320, Durham, NC 27708
xin.zhou@duke.edu (919) 660-2800
http://www.math.duke.edu/~zhou

Background
Education, Training, & Certifications
- Ph.D., University of Rochester 1988
- M.Sc., Chinese Academy of Sciences (China) 1982
Duke Appointment History
- Professor of Mathematics, Mathematics, Trinity College of Arts & Sciences 1999 - 2014
- Associate Professor with Tenure, Mathematics, Trinity College of Arts & Sciences 1995 - 1999
- Associate Professor, Mathematics, Trinity College of Arts & Sciences 1993 - 1995
Recognition
Awards & Honors
- Fellowship. John Simon Guggenheim Memorial Foundation. 1999
- George Polya Prize. Society for Industrial and Applied Mathematics. 1998
Research
Selected Grants
- Riemann-Hilbert Problem and Integrable Systems awarded by National Science Foundation 2006 - 2010
- Riemann-Hilbert problem and integrable systems awarded by National Science Foundation 2003 - 2007
- Inverse Scattering Theory awarded by National Science Foundation 2000 - 2003
- (97-0380) Inverse Scattering Theory awarded by National Science Foundation 1997 - 2000
- (94-0255) Inverse Scattering Theory awarded by National Science Foundation 1994 - 1997
Publications & Artistic Works
Selected Publications
- Academic Articles
  - "Janossy densities for unitary ensembles at the spectral edge." International Mathematics Research Notices 2008, no. 1 (December 1, 2008). Full Text
  - McLaughlin, KT-R, Vartanian, AH, and 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 11, no. 3-4 (November 2008): 187-364. Full Text
  - McLaughlin, KTR, Vartanian, AH, and Zhou, X. "Asymptotics of Laurent Polynomials of Odd Degree Orthogonal with Respect to Varying Exponential Weights." Constructive Approximation 27, no. 2 (March 2008): 149-202. Full Text
  - McLaughlin, KT-R, Vartanian, AH, and 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 100, no. 1 (January 2008): 39-104. Full Text
  - McLaughlin, KT-R, and 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 100 (2008): 39-104. (Academic Article)
  - Tovbis, A, Venakides, S, and Zhou, X. "Semiclassical focusing nonlinear schrödinger equation i: Inverse scattering map and its evolution for radiative initial data." International Mathematics Research Notices 2007 (December 1, 2007). Full Text
  - Deift, P, Its, A, Krasovsky, I, and Zhou, X. "The Widom–Dyson constant for the gap probability in random matrix theory." Journal of Computational and Applied Mathematics 202, no. 1 (May 2007): 26-47. Full Text
  - Vartanian, AH, and Zhou, X. "Asymptotics of Laurent polynomials of even degree orthogonal with respect to varying exponential weights." International Mathematics Research Papers 2006 (October 18, 2006). Full Text
  - Tovbis, A, Venakides, S, and Zhou, X. "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 59, no. 10 (October 1, 2006): 1379-1432. Full Text
  - Deift, P, Its, A, and Krasovsky, I. "The Widpm-Dyson constant for the gap probability in random matrix theory (Accepted)." a special edition of the Journal of Computational and Applied Mathematics (2006). (Academic Article)
  - McLaughlin, KT-R, and Vartanian, AH. "Asymptotics of Orthogonal Laurent Polynomials of Even Degree with Respect to Varying Exponential Weights (Accepted)." IMRN (2006). (Academic Article)
  - "On semiclassical (zero dispersion limit) solutions of the focusing nonlinear Schrödinger equation." Communications on Pure and Applied Mathematics 57, no. 7 (July 1, 2004): 877-985. Full Text
  - Deift, P, and Zhou, X. "Long-time asymptotics for solutions of the NLS equation with initial data in a weighted Sobolev space." Communications on Pure and Applied Mathematics 56, no. 8 (August 2003): 1029-1077. Full Text
  - Deift, P. "Long-time asymptotics for solutions of the NLS equation with initial data in a weighted Sobolev space." Comm. Pure Appl. Math. 56 (2003): 1-49. (Academic Article)
  - Niu, Q. "Interacting domain walls in an easy-plane ferromagnet." Physical Review B Condensed Matter and Materials Physics 65, no. 17 (May 1, 2002): 1724161-1724164. Full Text
  - Deift, P, and Zhou, X. "Perturbation theory for infinite-dimensional integrable systems on the line. A case study." Acta Mathematica 188, no. 2 (2002): 163-262. Full Text
  - Deift, P, and Zhou, X. "A priori L^p-estimates for solutions of Riemann-Hilbert problems." International Mathematics Research Notices , no. 40 (2002): 2121-2154.
  - Deift, P. "Uniform L^p estimates for solutions of Riemann--Hilbert Problems depending on external parameters." Intl. Math. Res. Notices , no. 40 (2002): 2121-2154. (Academic Article)
  - "Optimal tail estimates for directed last passage site percolation with geometric random variables." Advances in Theoretical and Mathematical Physics 5, no. 6 (November 1, 2001): 1-41.
  - Deift, P, Kriecherbauer, T, McLaughlin, KT-R, Venakides, S, and Zhou, X. "A Riemann–Hilbert approach to asymptotic questions for orthogonal polynomials." Journal of Computational and Applied Mathematics 133, no. 1-2 (August 2001): 47-63. Full Text
  - Baik, J, Deift, P, McLaughlin, KTR, and Miller, P. "Optimal tail estimates for directed last passage site percolation with geometric random variables." Adv. Theo. Math. Phys. 5, no. 6 (2001): 1207-1250. (Academic Article)
  - Deift, P, Kriecherbauer, T, McLaughlin, KT-R, Venakides, S, and Zhou, X. "Uniform asymptotics for polynomials orthogonal with respect to varying exponential weights and applications to universality questions in random matrix theory." Communications on Pure and Applied Mathematics 52, no. 11 (November 1999): 1335-1425. Full Text
  - Deift, P, Its, A, Kapaev, A, and Zhou, X. "On the Algebro-Geometric Integration¶of the Schlesinger Equations." Communications in Mathematical Physics 203, no. 3 (June 1, 1999): 613-633. Full Text
  - "Strong asymptotics of orthogonal polynomials with respect to exponential weights." Communications on Pure and Applied Mathematics 52, no. 12 (January 1, 1999): 1491-1552. Full Text
  - "Nonlinear magnetization dynamics of the classical ferromagnet with two single-ion anisotropies in an external magnetic field." Physical Review B Condensed Matter and Materials Physics 60, no. 18 (January 1, 1999): 12893-12911. Full Text
  - Cheng, PJ, Venakides, S, and Zhou, X. "Long-time asymptotics for the pure radiation solution of the sine—gordon equation." Communications in Partial Differential Equations 24, no. 7-8 (January 1999): 1195-1262. Full Text
  - "L²-Sobolev space bijectivity of the scattering and inverse scattering transforms." Communications on Pure and Applied Mathematics 51, no. 7 (January 1, 1998). Full Text
  - Deift, P, Venakides, S, and Zhou, X. "An extension of the steepest descent method for Riemann-Hilbert problems: the small dispersion limit of the Korteweg-de Vries (KdV) equation." Proceedings of the National Academy of Sciences of the United States of America 95, no. 2 (January 1998): 450-454. Full Text
  - Zhou, X. "L²-Sobolev space bijectivity of the scattering and inverse scattering transforms." Communications on Pure and Applied Mathematics 51, no. 7 (1998): X-730.
  - "New Results in Small Dispersion KdV by an Extension of the Steepest Descent Method for Riemann-Hilbert Problems." International Mathematics Research Notices , no. 6 (December 1, 1997): 284-299.
  - "Asymptotics for Polynomials Orthogonal with Respect to Varying Exponential Weights." International Mathematics Research Notices , no. 16 (December 1, 1997).
  - Deift, PA, Its, AR, and Zhou, X. "A Riemann-Hilbert Approach to Asymptotic Problems Arising in the Theory of Random Matrix Models, and also in the Theory of Integrable Statistical Mechanics." The Annals of Mathematics 146, no. 1 (July 1997): 149-149. Full Text
  - Deift, P, and Zhou, X. "Near integrable systems on the line: A case study-pertubation theory of the defocusing nonlinear Schrödinger equation." Mathematical Research Letters 4, no. 5 (1997): 761-772. Full Text
  - Xin, Z. "Strong regularizing effect of integrable systems." Communications in Partial Differential Equations 22, no. 3-4 (January 1997): 503-526. Full Text
  - Deift, P, Kamvissis, S, Kriecherbauer, T, and Zhou, X. "The Toda rarefaction problem." Communications on Pure and Applied Mathematics 49, no. 1 (January 1996): 35-83. Full Text
  - Deift, PA, and Zhou, X. "Asymptotics for the painlevé II equation." Communications on Pure and Applied Mathematics 48, no. 3 (1995): 277-337. Full Text
  - Xin, Z. "Inverse Scattering Transform for Systems with Rational Spectral Dependence." Journal of Differential Equations 115, no. 2 (January 1995): 277-303. Full Text
  - Deift, PA, and Zhou, X. "Long-time asymptotics for integrable systems. Higher order theory." Communications in Mathematical Physics 165, no. 1 (October 1994): 175-191. Full Text
  - Deift, P, Venakides, S, and Zhou, X. "The collisionless shock region for the long-time behavior of solutions of the KdV equation." Communications on Pure and Applied Mathematics 47, no. 2 (February 1994): 199-206. Full Text
  - Fokas, AS, Mugan, U, and Zhou, X. "On the solvability of Painleve I, III and V." Inverse Problems 8, no. 5 (October 1, 1992): 757-785. Full Text
  - Fokas, AS, and Zhou, X. "On the solvability of Painlevé II and IV." Communications in Mathematical Physics 144, no. 3 (March 1992): 601-622. Full Text
  - Deift, P, and Zhou, X. "A steepest descent method\\ for oscillatory Riemann-Hilbert problems." Bulletin of the American Mathematical Society 26, no. 1 (January 1, 1992): 119-125. Full Text
  - Deift, P, and Zhou, X. "Direct and inverse scattering on the line with arbitrary singularities." Communications on Pure and Applied Mathematics 44, no. 5 (July 1991): 485-533. Full Text
  - Zhou, X. "Inverse scattering transform for the time dependent Schrödinger equation with applications to the KPI equation." Communications in Mathematical Physics 128, no. 3 (March 1990): 551-564. Full Text

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Education, Training, & Certifications

Duke Appointment History

Awards & Honors

Selected Grants

Selected Publications

Academic Articles