Algebro-geometric initial value problems for discrete matrix mKdV equations: Tetragonal curves and Riemann theta function solutions
报告题目(Title)：Algebro-geometric initial value problems for discrete matrix mKdV equations: Tetragonal curves and Riemann theta function solutions
报告人(Speaker)：耿献国 教授（郑州大学）
地点(Place)：后主楼1225
时间(Time)：2026年10月20日（周二）13:30-14:30
邀请人(Inviter)：王灯山
报告摘要
This talk develops the theory of tetragonal curves and introduces a systematic method for obtaining Riemann theta function solutions to algebro-geometric initial value problems for discrete matrix modified Korteweg-de Vries equations. In particular, the Lax pair of the discrete matrix modified Korteweg-de Vries hierarchy is derived from a discrete 4 × 4 matrix spectral problem using the discrete zero-curvature equation and Lenard equations. Then, we introduce the corresponding tetragonal curve and its Riemann theta function through the characteristic polynomial of the discrete Lax matrix, and also discuss the construction of three kinds of Abelian differentials. Building on the theory of tetragonal curves, we investigate algebro-geometric properties of Baker-Akhiezer functions and fundamental meromorphic functions. Finally, Riemann theta function solutions for the entire discrete matrix modified Korteweg-de Vries hierarchy are derived via asymptotic analysis.
主讲人简介
耿献国，郑州大学数学与统计学院，二级教授、原院长，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，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。
