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Application of tetragonal curves to the hierarchy of extended Volterra lattices

耿献国 教授

郑州大学

报告时间：2026年10月20日（星期二）15：30--16：30

报告地点：国实E802

报告摘要：

The theory of tetragonal curves is applied to the study of discrete integrable systems. Based on the discrete Lenard equation, we derive a hierarchy of extended Volterra lattices associated with the discrete 4×4 matrix spectral problem. Resorting to the characteristic polynomial of the Lax matrix for the hierarchy of extended Volterra lattices, we introduce a tetragonal curve, a Baker-Akhiezer function, and 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 the origin and two infinite points. The straightening out of various flows is precisely given by utilizing the Abel map and the meromorphic differential. We finally obtain Riemann theta function solutions of the entire hierarchy of extended Volterra lattices.

报告人简介：耿献国，郑州大学数学与统计学院，二级教授，博士生导师，郑州大学特聘教授。国务院政府特殊津贴专家，河南省优秀专家，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., SIAM J. Math. Anal., Int. Math. Res. Not. IMRN 等刊物上发表论文。主持2项国家自然科学基金重点项目和多项国家自然科学基金面上项目等。获得河南省自然科学一等奖和河南省科学技术进步奖二等奖各一项，所带领的研究团队被评为河南省可积系统及应用研究创新型科技团队。

邀请人： 王振

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