题目：Spectral invariants for vector periodic NLS

内容简介：We consider a first order operator with a periodic 3x3 matrix potential on the real line. This operator appears in the problem of the periodic vector NLS equation.  The spectrum of the operator covers the real line, it is union of the spectral bands of multiplicity 3, separated by intervals of multiplicity 1. The main results of this work are the following:

1) The Lyapunov function on the corresponding 2 or 3-sheeted Riemann surface is described.

2) Necessary and sufficient conditions are given when the Riemann surface is 2-sheeted.

3) The asymptotics of 2-periodic eigenvalues are determined.

4) One constructs an entire function, which is positive on the spectrum of multiplicity 3 and is negative on its gaps.

5) The estimate of the potential in terms of gap lengths is obtained.

6) The Borg type results about inverse problems are solved.

7) The solution of the periodic vector NLS equation for the case of the 2-sheeted Riemann surface is described.

报告人：Evgeny Korotyaev

报告人简介：Evgeny Korotyaev教授是谱理论与可积系统、散射理论领域的国际知名数学家。他现任圣彼得堡国立大学数学-力学系教授，兼任俄罗斯高等经济研究大学教授，并受聘为东北师范大学前沿交叉研究院教授。Korotyaev教授于1982年在圣彼得堡国立大学获博士学位，1996年在圣彼得堡Steklov研究所获理学博士学位。三十余年来，他专注于逆谱理论、几何函数论、可积系统与周期介质上的Dirac算子与Schrodinger算子等方向的研究，在Invent. Math., J. Reine Angew. Math., Math. Ann., Commun. Math. Phys., Trans. Am. Math. Soc., Inverse Probl., JFA, JDE等顶级期刊发表论文160余篇，Google Scholar引用量逾3200次。

时间：2026年3月16日(周一) 16：00开始

地点：石牌校区南海楼224会议室

热烈欢迎广大师生参加!