Riemann-Hilbert Methods and Frontiers of Computer Mathematics

Riemann-Hilbert Methods and Frontiers of Computer Mathematics

Introduction

Riemann-Hilbert problem is one of 23 famous problems raised by Hilbert at Paris International Mathematician Congress in 1900. Complex analysis has been introduced to solve the problem by linear Lax of the spectrum parameters in nonlinear integrable systems, thus, the integrable nonlinear evolution system is transformed into a Riemann-Hilbert problem for finding an analytic function with a particular jump form on a given curve. In the 80s of the last century, the Riemann-Hilbert problem was used as a more general tool than the inverse scattering method to study integrable systems. In 1992, Fokas and Its established the connection between orthogonal polynomials and Riemann-Hilbert problems; In 1993, Deift and Zhou from American Academy of Sciences made Its's method more systematical and rigorist, they also came up with better nonlinear descent method to transform the long time asymptotic analysis of the initial value problem of the KdV equation of Schwartz type into a scalar Riemann-Hilbert problem; In1999, the nonlinear descent method was been used to study the universality problem in random matrix by Deift. At the international Conference on integrable systems and stochastic matrices and applications in 2006, Deift(invited to report on an international mathematician conference twice), academician from American Academy of Sciences, put forward problems of integrable systems, random matrix and 16 open problems of Riemann-Hilbert problem, such as KdV equation with quasi-periodicity initial value, Riemann-Hilbert problems with non-analytical data, perturbation theory and initial boundary value problem of infinite dimensional integrable system, etc.

 

At the moment, it is popular to use the Riemann-Hilbert method to study integrable system and random matrix in the field of international mathematical physics, at the same time, it is also closely related to computer mathematics since many important reasoning processes need to be carried out by symbolic computation. The study of this direction not only has important theoretical significance, but also has significant application value in many nonlinear science fields.

 

International well-known experts including professor Alexander R. Its (Indiana university, USA), professor A. S. Fokas (University of Cambridge, UK), professor B. A. Malomed (Tel Aviv University, Israel) and some other experts on integrable systems in China are invited to the forefront seminar to discuss the important frontiers of Riemann-Hilbert problems, stochastic matrices, integrable systems and computer mathematical, young talents can have better understanding and mastering for these frontier issues through the discussion, it may also promote the development of integrable system, random matrix, Riemann-Hilbert problem, computer mathematics and other related fields for domestic scholars.

 

Provisional time: 2017.12.9-2017.12.15

 

Leading official and organizing committee (usually composed of 2 people):

Yong Chen (East China Normal University), Zhenya Yan (Institute of mathematics, CAS, coordinator)