报告题目：Identities in twisted Brauer and twisted partition monoids
报告人：Mikhail Volkov 教授 俄罗斯乌拉尔联邦大学邀请人：杨丹丹 教授
报告时间：2023年11月8日（周三）14：00-16：15（共3个学时）
报告地点： 南校区会议中心121会议室
报告人简介：
Mikhail Volkov教授于1994年在圣彼得堡大学获得俄罗斯国家博士学位（Doctor of Science degree in Mathematics），他长期担任乌拉尔国立大学代数与理论计算机科学研究所所长，2016年首位当选俄罗斯教育部首届俄罗斯联邦数学讲席教授，2017年当选芬兰科学与文学院外籍院士，2019年被德国研究基金遴选为Mercator教授。他是几个著名的理论计算机年度会议永久执行委员，是Semigroup Forum执行主编和多份国际杂志编委。他是自动机理论，字上组合学，半群与形式语言等重要研究方向上的研究领袖，谷歌学术引用近2500次，相关工作多次入选理论计算机顶级会议，并曾两次在CIAA会议获得最佳论文奖。
报告摘要：
Partition or diagram monoids first appeared in 1937 in a paper by Brauer in which they served as vector space bases of certain associative algebras relevant in representation theory of classical groups. Other species of diagram monoids were invented by Temperley and Lieb in the context of statistical mechanics in the 1970s and by Kauffman and Jones in the context of knot theory in the 1980s. Since then diagram monoids have revealed many other connections, e.g., with low dimensional topology, topological quantum field theory, quantum groups etc. Recently, they have been intensively studied as purely algebraic objects, and these studies have shown that diagram monoids are quite interesting from this viewpoint as well.

We report recent results on the complexity of checking identities in some infinite diagram monoids, including Kauffman, twisted Brauer and twisted partition monoids. Some of them are shown to have coNP-complete identity checking; this gives a very first example of a "natural" infinite monoid with difficult identity checking.
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