报告题目:Tetragonal curves and algebro-geometric solutions of the Blaszak-Marciniak lattices

报告人：耿献国 教授 (郑州大学)

报告时间：2022年10月15日 周六上午 9：00-10：00

报告地点：腾讯会议 157501420

摘要：

The theory of tetragonal curves is first applied to the study of discrete integrable systems. Based on the discrete Lenard equation, we derive a hierarchy of Blaszak-Marciniak lattice equations associated with the 4×4 matrix spectral problem. Resorting to the characteristic polynomial of the Lax matrix for the hierarchy of Blaszak-Marciniak lattice equations, we introduce a tetragonal curve, a Baker-Akhiezer function, and three meromorphic functions on it. We study algebro-geometric properties of the tetragonal curve and asymptotic behaviors of the Baker-Akhiezer function and meromorphic functions near two infinite points. The straightening out of various flows is exactly given by means of the Abel map and the meromorphic differential. We finally obtain algebro-geometric solutions of the entire Blaszak-Marciniak lattice hierarchy.

报告人简介：

耿献国，郑州大学数学与统计学院教授，博士生导师，郑州大学特聘教授。国务院政府特殊津贴专家，全国百篇优秀博士学位论文指导老师。从事的研究方向是可积系统及应用。曾在Commun. Math. Phys., Trans. Amer. Math. Soc., Adv. Math., J. Nonlinear Sci., SIAM J. Math. Anal., Int. Math. Res. Not. IMRN, Nonlinearity等刊物上发表论文。主持国家自然科学基金重点项目2项和多项国家自然科学基金面上项目等。

邀请人： 马立媛