科学研究

当前位置:首页 > 科学研究 > 学术预告 > 正文

2023年报告23:郑州大学耿献国教授:Algebro-geometric quasi-periodic solutions to the hierarchy of extended Volterra lattices

时间:2023-04-18 08:41:26 来源: 作者: 阅读:

报告题目:Algebro-geometric quasi-periodic solutions to the hierarchy of extended Volterra lattices

报告人:耿献国

报告时间:2023419日(周三)15:00-17:00

报告地点:数学楼315会议室

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,二级教授,博士生导师。郑州大学学科特聘教授,国家天元数学中部中心学术委员会委员。国务院政府特殊津贴专家,河南省优秀专家。2003年被评为河南省特聘教授, 获全国百篇优秀博士学位论文指导老师,所指导的博士研究生学位论文获得全国优秀博士学位论文一篇、河南省优秀博士学位论文六篇。2016年获河南省科技进步二等奖,2022年获河南省自然科学奖一等奖。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。曾在Commun. Math. Phys., Trans. Amer. Math. Soc., Adv. Math., SIAM J. Math. Anal., Int. Math. Res. Not.等刊物上发表论文。现主持1项国家自然科学基金重点项目,曾主持完成1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。20052月至20173月任威廉希尔经理。