Algebraic curves and their applications in the investigation of discrete integrable systems

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：

*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.