讲座题目：孤子方程和黎曼希尔伯特方法

讲座人: Spyridon Kamvissis 教授

讲座时间：09:30

讲座日期：2015-6-23

地点：长安校区 文津楼三段612室

主办单位：太阳成集团tyc4633 计算智能团队

讲座内容：

The asymptotic analysis of so-called completely integrable PDEs is often reducible to the asymptotic analysis of Riemann-Hilbert matrixfactorization problems in the complex plane or a Riemann surface. This is achieved through a deformation method, initiated by Its, and madesystematic and rigorous by Deift and Zhou. Although it is often known as the nonlinear steepest descent method,it is only fairly recently that the term "steepest descent" has been justified, properly speaking steepest descent contours have been constructed, and the method has achieved it full power. In my talk I will illustrate this asymptotic method by considering the case of the semiclassical focusing NLS problem. I will explain how the nonlinear steepest descent method gives rise to a maxi-min variational problem for Green potentials with external field in an infinite sheeted Riemann surface and I will describe results on existence and regularity of solutions to this variational problem. The solutions are the steepest descent contours (S-curves; trajectories of quadratic differentials) together with their equilibrium measures.

讲座人简介：

Spyridon Kamvissis received his B.Sc. and Ph.D. degrees in mathematics from, respectively, Imperial College, University of London, in 1984, and Courant Institute, New York University, in 1991.He learned from famous mathematician of Peter Lax and Percy Deift who is the academician of American academy of science. He is now a full professor in the direction of Mathematical physics & integrable system, University of Crete of Greece. Before joining University of Crete, he worked in the  Department of Mathematics, University of Patras from 1999 to 2001,and in the Max-Planck Institutes of Mathematics as a researcher from 2002 to 2005.As a Visiting Professor, he has visited the University of Maryland, University of Cambridge, Institute Mittag-Leffler and University of Vienna. He, as a visiting scholar, also visited the Mathematical Sciences Research Institute of Berkeley, Institute for Advanced Study of Princeton, Erwin Schrodinger Institute and University of Vienna and so on.

His research interests are mainly in exact solutions of soliton equations and asymptotic theory.He’s methods include the analysis of Riemann-Hilbert factorization problems on the complex plane or a hyperelliptic Riemann surface and variational problems for logarithmic potentials with external fields. He is working on the generalises classical theory of stationary phase and steepest descent. Some of his most important work has beenpublished in international journals and international conferences.