报告学者：金贤安
报告者单位：厦门大学，教授
报告时间：2022年4月26日（周二）9:00-10:00
报告地点：线上腾讯会议，会议ID:544-804-163
报告摘要：The interior polynomial and the exterior polynomial, introduced in [1], are generalizations of valuations on (x,1) and (1,y) of the Tutte polynomial T_G(x,y) of graphs to hypergraphs, respectively. The top of the HOMFLY polynomial of a special alternating link coincides with the interior polynomial of the pair of hypergraphs induced by the Seifert graph of the link.
In this talk, we will give a detailed account of definitions of these two polynomials, their relations with the Tutte polynomial in graph theory and the HOMFLY polynomial in knot theory. The two polynomials are defined under a fixed ordering of hyperedges, and are proved to be independent of the ordering using techniques of polytopes in [1]. Similar to the Tutte's proof of his polynomial, we then provide a direct and elementary proof for the well-definedness of the interior and exterior polynomials of hypergraphs. See [2] for details.
References:
[1] T. Kalman, A version of Tutte's polynomial for hypergraphs, Adv. Math. 244 (2013) 823-873.
[2] X. Guan, X. Jin, T. Ma，A direct and elementary proof of the well-definedness of the interior and exterior polynomials of hypergraphs, arXiv:2201.12496[math.CO].
报告人简介： 金贤安，厦门大学教授，博士生导师。主要从事图论、纽结论及其应用等研究工作，已在包括AAM、JCTA、JGT、PAMS等在内的国际著名学术期刊发表学术论文60余篇。主持国家自然科学基金项目4项、参加国家自然科学基金重点项目1项和数学天元基金项目3项。多次在国内国际会议作大会报告和邀请报告。长期从事《离散数学》、《图论》与《拓扑学》等课程教学工作，其中《离散数学》入选福建省一流线上课程和一流线上线下混合式课程。主持完成教育部拔尖计划研究课程1项、参加2项。已培养和正培养访问学者、博士后、博士、硕士、“拔尖计划”本科生、“英才计划”中学生50多名。