走向现代数学学术报告 - 金贤安教授（No. 798)

报告题目：Twist polynomial as a weight system

报 告 人：金贤安 教授（厦门大学）

邀 请 人：胡丹 博士

报告时间：2025年6月7日 15:00

报告地点：东海岸校区-D实315

报告摘要：This talk contains five parts. First we give a brief introduction to the knot theoretic background. In the second part, we give the definitions of ribbon graphs and their partial-dual (genus) polynomials, and some progress in this topic. Then based on Chmutov's work we prove the partial dual polynomial as a function of framed chord diagrams satisfies three four-term relations, thus can be viewed as a weight system. In the fourth part, we extend the above results to set systems and their twist (width) polynomials, i.e. introduce the 4-term relation of set systems and prove the twist polynomial satisfies it. In the last part, its connection with Hopf algebra is discussed.

个人简介：金贤安，厦门大学教授、博士生导师。厦门大学本科和博士、北京大学博士后。主要从事图论、纽结论、拟阵论和数学化学等方面的研究工作，已在Forum Math. Sigma、Fund. Math. 、PAMS、AAM、JCTA、JGT等数学期刊及NC、JSP、JTB等交叉学科期刊发表学术论文90多篇。先后主持国家自然科学基金项目4项，参加重点项目1项。主持国家级一流课程1门、教育部拔尖计划研究课题2项。曾应邀在美国第33届国际拓扑及其应用大会作50分钟报告等。曾获宝钢优秀教师奖和国家教学成果二等奖等。已培养博士生11人和硕士生28人。现兼任福建省运筹学会秘书长等。