报告题目 (Title)：Space curves and solitons of the KP hierarchy （空间曲线与KP方程的孤立子）

报告人 (Speaker)： 谢远成 博雅博士后（北京大学）

报告时间 (Time)：2023年11月23日(周四) 11:00-13:00

报告地点 (Place)：校本部 F309

邀请人(Inviter)：张大军 教授

主办部门：理学院数学系

报告摘要：It is well known that algebro-geometric solutions of the KdV hierarchy are constructed from the Riemann theta (or Klein sigma) functions associated with hyperelliptic curves, and soliton solutions can be obtained by rational limits of the corresponding curves. In this talk, I will associate a family of singular space curves indexed by the numerical semigroups $\langle l, lm+1, \dots, lm+k \rangle$ where $m \ge 1$ and $1 \le k \le l-1$ with a class of generalized KP solitons. Some of these curves can be deformed into smooth ``space curves", and they provide canonical models for the $l$-th generalized KdV hierarchies (KdV hierarchy corresponds to the case $l = 2$). If time permits, we will also see how to construct the space curves from a commutative ring of differential operators in the sense of the well-known Burchnall-Chaundy theory. This talk is based on a joint work with Professor Yuji Kodama.