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博学堂讲座预告(第470讲)

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报告题目:Algebraic curves and their applications in the investigation of discrete integrable systems

报告时间:20191023日下午3:45-4:30(周三)

报告地点:教师活动中心

报告人:耿献国教授 (郑州大学)

摘要:In this talk, we introduce the concept of algebraic curves and discuss their basic properties,

including the calculation of genus of algebraic curve, properties at infinity, and the construction

of three kinds of Abel differentials, and others. As an illustration, the hierarchy of Bogoyavlensky

lattices associated with a discrete 3×3 matrix spectral problem are firstly derived. Based on the

characteristic polynomial of Lax matrix for the hierarchy of stationary Bogoyavlensky lattices,

we derive the corresponding trigonal curve and a basis of holomorphic differentials on it, from

 which we construct the Riemann theta function, the related Baker–Akhiezer function, and an

algebraic function carrying the data of the divisor. The Riemann theta function representations

of the Baker–Akhiezer function, the meromorphic function, and in particular, that of solutions

of the hierarchy of Bogoyavlensky lattices are finally obtained

报告人概况:

耿献国,郑州大学数学与统计学院教授,博士生导师,郑州大学学科特聘教授。河南省数学会理事长,国务院政府特殊津贴专家,2012年获全国百篇优秀博士学位论文引导老师。从事的研究方向是可积系统及应用。曾在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。

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