报告题目：The lowest upper bound on the number of zeros of a class of hyperelliptic Abelian integrals

报告人：孙杨剑副教授，上饶师范学院

报告时间：2025年11月21日（周五）10:30

报告地点：20-200

报告摘要：In this talk, we devoted to the number of isolated zeros of the hyperelliptic integrals, where is a compact component of the hyperelliptic cures, here, is a maximal open interval on which a continuous family of ovals exists, and is a polynomial of with degree five. As is shown in Liu and Xiao (2013), can be assumed to have the form and there exist some real numbers and such that has at least two isolated zeros if. However, the problem whether two is also the upper bound of the number of isolated zeros of  remains open for . In this paper, we propose a new simplification technique, which can reduce the degree of a polynomial by at least half. This combined with the new criterion and some available methods and techniques shows that two is indeed the lowest upper bound on the number of isolated zeros of for some subset of, which partially gives a positive answer to the open problem. The methods and techniques developed in this paper may be used to study other similar problems.

报告人简介：孙杨剑，上饶师范学院副教授。主要从事常微分方程定性理论的研究。主持国家自然科学基金项目、江西省教育厅项目各一项，以第一作者或通讯作者身份在Sci. China Math.、Phys. D、Proc. Royal. Soc. Edinb. Sec. Math、Bull. Sci. Math.、Dis. Con. Dyn. Sys. B等SCI杂志上发表论文十余篇。

邀请人：戴燕飞