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Algebraic curves and their applications in the investigation of discrete integrable systems
耿献国 教授(郑州大学)
2020年8月25日 8:00-9:30  腾讯会议ID:125 581 580

*主持人:陈勇 教授
*时间:2020年8月25日 8:00-9:30
*地点:腾讯会议ID:125 581 580

*主讲人简介:
耿献国:教授,博士生导师,研究方向为可积系统及应用。现任郑州大学学科特聘教授?学科方向带头人,河南省数学会理事长。获国务院政府特殊津贴,河南省优秀专家。2003年被评为河南省特聘教授,2012年获全国百篇优秀博士学位论文指导老师,2016年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, 2016年获河南省科技进步二等奖。曾在Trans. Amer. Math. Soc., Adv. Math., J. Nonlinear Sci., SIAM J. Math. Anal., Int. Math. Res. Not. IMRN, Nonlinearity,J. Differential Equations等刊物上发表论文。现主持国家自然科学基金重点项目1项,曾主持完成国家自然科学基金重点项目1项和国家自然科学基金面上项目6项,承担完成国家重点基础性研究发展规划(973规划)子项目1项等。

*讲座内容简介:
On the basis of the characteristic polynomials of Lax matrixes for the soliton hierarchies, we introduce the corresponding algebraic curves, including the hyperelliptic curve, trigonal curve, and tetragonal curve. We study the calculation of genus of algebraic curve, properties at infinity, and the construction of three kinds of Abel differentials. We establish the corresponding Baker-Akhiezer functions and meromorphic functions. The straightening out of various soliton flows is exactly given through the Abel map and Abel-Jacobi coordinates. Using the theory of algebraic curves, we obtain the explicit Riemann theta function representations of the Baker-Akhiezer function and the meromorphic function. As an illustration, we arrive at algebro-geometric solutions for the hierarchy of Bogoyavlensky lattices.