Xin Zhou, Professor

Contact Info:

Office Location:	109 Physics Building
Office Phone:	(919) 660-2842
Email Address:
Web Page:	http://www.math.duke.edu/~zhou

Teaching (Fall 2008):

• MATH 103.04, INTERMEDIATE CALCULUS Synopsis

  Physics 130, TuTh 01:15 PM-02:30 PM

• MATH 242.01, FUNCTIONAL ANALYSIS

  Physics 227, TuTh 11:40 AM-12:55 PM

• MATH 204.01, BASIC ANALYSIS II Synopsis

  Physics 227, TuTh 11:40 AM-12:55 PM

Education:

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

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.

Curriculum Vitae

Recent Publications   (More Publications)

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. (Accepted, 2006)
2. with K. McLaughlin , A.H. Vartanian, Asymptotics of Orthogonal Laurent Polynomials of Odd Degree with Respect to Varying Exponential Weights, Constructive Approximation (Accepted, 2006)
3. B. Rider and X. Zhou, Janossy densities for unitary ensembles at the spectral edge (Preprint, 2006)
4. 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 (Submitted, 2006)
5. with A. Tovbis and S. Venakides, Semiclassical focusing nonlinear Schroedinger equation I: Inverse scattering map and its evolution for radiative initial data, completed (Submitted, 2006)

Recent Grant Support

• Riemann-Hilbert Problem & Integrable Systems, National Science Foundation, DMS-03-00844, 2003/07-2006/06.      

Conferences Organized

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