Curriculum Vitae

Xin Zhou

109 Physics Building
Durham, NC 27708 		(919) 660-2842 (office)
(email)
Education

Ph.D.in Mathematics, 1988, University of Rochester
M.S.in Physics, 1982, Chinese Academy of Sciences (Institute of Physics)

Areas of Research

Partial Differential Equations and Integrable Systems

Awards, Honors, and Distinctions

Polya Prize, 1998
Guggenheim Fellowship 1999

Major Grant Support

NSF Analysis

Recent Grant Support

Conferences Organized

Special session on Random Matrices, XXIII International Conference of Differential Geometric Methods in Theoretical Physics, August, 2005  
ORGANIZER, SIAC-SIAM mini-symposium 10/1/2004, December 2004  
organizer, NSF- AMS Summer Conference Snowbird UT, June 2003  
Professional Service

Qualifying Exam Committee for Sergei Below, December 2006  
Exam Committee for Shu Dai, December 2005  
ARP search committee, December 2004  
Review committee for Huber, December 2004  
Qualifying exam for Abe Smith, November 03, 2004  
Qualifying for Xu Feng, March, 2004  
Appl. Panel, January 2003  
Selected Recent Invited Talks

AMS, Alabama, 1 July 2001  
Invited Addresses: Conference at the University of Montreal, 2000. AMS SouthEast Meeting, 2000.

Publications

Papers Published

  1. with K. T.-R. McLaughlin, A. H. Vartanian, Asymptotics of Orthogonal Laurent Polynomials of Even Degree with Respect to Varying Exponential Weights, IMRP (2006)
  2. with P. Deift, Riemann-Hilbert Problem, in Encyclopedia of Nonlinear Science, edited by A.Scott (2005), pp. 804-808
  3. with P. Deift, Random Matrix Theory III, in Encyclopedia of Nonlinear Science, edited by A.Scott (2005), pp. 771-774
  4. Alexander Tovbis, Stephanos Venakides, X. Zhou, On Semiclassical (Zero Dispersion Limit) Solutions of the Focusing Nonliner Schroedinger Equation, Comm. Pure Appl. Math., vol. 57 (2004), pp. 877-985
  5. with P. Deift, Long-time asymptotics for solutions of the NLS equation with initial data in a weighted Sobolev space, Comm. Pure Appl. Math., vol. 56 (2003), pp. 1-49
  6. with P. Deift, Perturbation theory for infinite dimensional integrable systems on the line. A case study, Acta Math, vol. 188 (2002), pp. 163-262
  7. with P. Deift, Uniform L^p estimates for solutions of Riemann--Hilbert Problems depending on external parameters, Intl. Math. Res. Notices no. 40 (2002), pp. 2121-2154
  8. with P.Deift, T.Kriecherbauer, K. T-R. McLaughlin, and S.Venakides, A Riemann-Hilbert approach to asymptotic questions for orthogonal polynomials, J. Comput. Appl. Math., vol. 133 no. 1-2 (2001), pp. 47-63
  9. with J.Baik, P.Deift, K. T-R. McLaughlin, and P.Miller, Optimal tail estimates for directed last passage site percolation with geometric random variables, Adv. Theo. Math. Phys., vol. 5 no. 6 (2001), pp. 1207-1250
  10. Percy Deift and Xin Zhou, Perturbation theory for infinite dimensional integrable systems on the line. A case study, ACTA Math. preprint 2000
  11. with P. Deift, A. Its, and A. Kapaev, On the algebro-geometric integration of the Schlesinger equations, Comm. Math. Phys. 203 (1999), no. 3, 613-633.
  12. with P. Chen and S. Venakides, Long time asymptotics for pure radiation solution of the sine-Gordon equation, Comm. in PDE 24 (1999), no.7-8, 1195-1262.
  13. with P. Deift, T. Kriecherbauer, K. McLaughlin, and S. Venakides, Uniform asymptotics for polynomials orthogonal with respect to varying exponential weights and applications to universality questions in random matrix theory, Comm. Pure Appl. Math. 52 (1999), no. 11, 1335-1425.
  14. with P. Deift, T. Kriecherbauer, K. McLaughlin, and S. Venakides, Strong asymptotics for polynomials orthogonal with respect exponential weights, an announcement, Comm. Pure Appl. Math. 52 (1999), no. 12, 1491-1552.
  15. with P. Deift, Asymptotics for Oscillatory Riemann-HilbertProblems, CCAST (Beijing), Proc. CCAST, 1999.
  16. P. Deift, S. Venakides, Xin Zhou, An extension of the steepest descent method for Riemann-Hilbert problems: the small dispersion limit of the Korteweg-de Vries, Proc. Natl. Acad. Sc. USA, 95, no. 2, 450-454 (1998)
  17. Xin Zhou, The L2-Sobolev space bijectivity of the scattering and inverse scattering transforms, Comm. Pure Appl. Math., vol. LI, 697-731 (1998)
  18. P. Deift, T. Kriecherbauer, K. McLaughlin, S. Venakides,Xin Zhou, Uniform Asymptotics for Orthogonal Polynomials, Proceedings of the International Congress of Mathematicians, Vol. III (Berlin), 1998.
  19. Xin Zhou, Strong regularizing effect of integrable systems, Comm. in PDE, 22, no. 3-4, 503-526 (1997).
  20. P. Deift, A. Its, Xin Zhou, A Riemann-Hilbert problem approach to asymptotic problems arising in the theory of random matrix models, and also in the theory of integrable statistical mechanics, Ann. of Math. 146, no. 1, 149-235 (1997)
  21. P. Deift, S. Venakides, Xin Zhou, New results in small dispersion KdV by an extension of the steepest descent method for Riemann-Hilbert problems, IMRN, 6 (1997), 286-299.
  22. P. Deift, T. Kriecherbauer, K. McLaughlin, S. Venakides, Xin Zhou, Asymptotics for polynomials orthogonal with respect to varying exponential weights, IMRN, 16, 759-782 (1997)
  23. P. Deift, Xin Zhou, Near integrable systems on the line. A case study-perturbation theory of the defocusing nonlinear Schroedinger equation, Math. Res. Lett. 4, no. 5, 761-772 (1997).
  24. P. Deift, S. Kamvissis, T. Kriecherbauer, Xin Zhou, The Toda rarefaction problem, Comm. Pure Appl. Math. XLIX, no. 1, 35-83 (1996).
  25. Xin Zhou, Inverse scattering transform for systems with rational spectral dependence, Jour. Diff. Eq., 115(2), 277-303 (1995)
  26. P. Deift, Xin Zhou, Asymptotics for the Painleve II equation, Comm. Pure Appl. Math. 48, no. 3, 277-337 (1995).
  27. P. Deift, Xin Zhou, Long-time asymptotics for integrable systems. Higher order theory, Comm. Math. Phys. 165, no. 1, 175-191 (1994)
  28. Deift, P. and Xin Zhou, Long-time asymptotics for the autocorrelation function of the transverse Ising chain at the critical magnetic field, Singular limits of dispersive waves (Lyon, 1991), 183-201, NATO Adv. Sci. Inst. Ser. B Phys. 320, Plenum, New York, 1994.
  29. Deift, P., Venakides, S. and Xin Zhou, The collisionless shock region for the long-time behavior of solutions of the KdV equation, Comm. Pure Appl. Math. 47(2) (1994), 199-206
  30. Deift, P. and Xin Zhou, Asymptotics for the Painleve II equation: announcement of result, Spectral and scattering theory and applications, 17-26, Adv. Stud. Pure Math. 23, Math. Soc. Japan, Tokyo, 1994
  31. Beals, R., Deift, P., and Xin Zhou, The inverse scattering transform on the line, Important Developments in Soliton Theory, 7-32, Springer Ser. Nonlinear Dynam., Springer, Berlin, 1993.
  32. Deift, P., Its, A. and Xin Zhou, Long-time asymptotics for integrable nonlinear wave equations, Important Developments in Soliton Theory, 181-204, Springer Ser. Nonlinear Dynam., Springer, Berlin, 1993
  33. Deift, P. and Xin Zhou, A steepest descent method for oscillatory Riemann-Hilbert problems. Asymptotics for the MKdV equation, Ann. of Math. (2) 137 (1993), 295-368
  34. Fokas, A., Mugan, U. and Xin Zhou, On the solvability of Painleve I, III and V, Inverse Problems 8 (1992), no. 5, 757-785
  35. Fokas, A. and Xin Zhou, On the solvability of Painleve II and IV, Comm. Math. Phys. 144 (3) (1992), 601-622
  36. Deift, P. and Xin Zhou, A steepest descent method for oscillatory Riemann-Hilbert problems, Bull. Amer. Math. Soc. (N.S.) 26 (1992), no. 1, 119-123
  37. Deift, P. and Xin Zhou, Direct and inverse scattering on the line with arbitrary singularities, Comm. Pure Appl. Math. 44 (1991), 485-533
  38. Fokas, A., Its, A. and Xin Zhou, Continuous and discrete Painleve equations, Painleve transcendents (Sainte-Adele, PQ, 1990), 34-47, NATO Adv. Sci. Inst. Ser. B Phys., 278, Plenum, New York, 1992
  39. Xin Zhou, Inverse scattering transform for the time dependent Schrodinger equation with applications to the KPI equation, Comm. Math. Phys. 128 (1990), 551-564
  40. Xin Zhou, Direct and inverse scattering transforms with arbitrary spectral singularities, Comm. Pure Appl. Math. 42 (1989), 895-938
  41. Xin Zhou, The Riemann-Hilbert problem and inverse scattering, SIAM J. Math. Anal. 20 (1989), 966-986
  42. Pu, F., Li, B. and Xin Zhou, Multisoliton solutions for a classical ferromagnetic chain, Comm. Theoret. Phys. 2 (1983), 797-802

Papers Accepted

  1. with A. Tovbis, S. Venakides, On the long time limit of semiclassical (zero dispersion limit) solutions of the focusing Nonlinear Schroedinger Equation: Pure radiation case.,, Comm. Pure Appl. Math. (2006)
  2. with K. McLaughlin , A.H. Vartanian, Asymptotics of Orthogonal Laurent Polynomials of Odd Degree with Respect to Varying Exponential Weights, Constructive Approximation (2006)
  3. with P. Deift, A. Its, I. Krasovsky, The Widpm-Dyson constant for the gap probability in random matrix theory, a special edition of the Journal of Computational and Applied Mathematics (2006)

Papers Submitted

  1. 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 (2006)
  2. with A. Tovbis and S. Venakides, Semiclassical focusing nonlinear Schroedinger equation I: Inverse scattering map and its evolution for radiative initial data, completed (2006)

Papers In Preparation

  1. A.S. Fokas and X. Zhou, Linearly Moving Boundry Value Problems (2005)

Preprints

  1. B. Rider and X. Zhou, Janossy densities for unitary ensembles at the spectral edge (2006)
  2. K. T.-R. McLaughlin, A. H. Vartanian, and X. Zhou, Variational Problems Associated with the Asymptotic Study of Orthogonal Rational Functions: The Riemann-Hilbert Problem Approach, completed (2005)
  3. N. Huang, W. Liu, F. Pu, , W. Zhang, Xin Zhou, Nonlinear magnetization dynamics of a ferromagnet with an anisotropy in an external magnetic field, 1997 , preprint 1997
Last modified: 2006/12/15