应兰州大学数学与统计学院邀请，俄罗斯乌拉尔联邦大学的 Mikhail Volkov 教授和 SergeyGusev 高级研究员将进行线下学术报告，欢迎全校师生参加。

报告时间：2023年11月10日(星期五)下午3:00

报告地点：理工楼631

报告题目一：Identities in twisted Brauer and twisted partition monoids

报告人：Mikhail Volkov教授

报告摘要：Partition or diagram monoids first appeared in 1937 in a paperby Brauer in which they served as vector space bases of certainassociative algebras relevant in representation theory ofclassical groups. Other species of diagram monoids wereinvented by Temperley and Lieb in the context of statisticalmechanics in the 1970s and by Kauffman and Jones in the contextof knot theory in the 1980s. Since then diagram monoids haverevealed many other connections, e.g., with low-dimensionaltopology, topological quantum field theory, quantum groups etc.Recently, they have been intensively studied as purely algebraicobjects, and these studies have shown that diagram monoids arequite interesting from this viewpoint as well.

We report recent results on the complexity of checking identitiesin some infinite diagram monoids, including Kauffman, twisted Brauerand twisted partition monoids. Some of them are shown to havecoNP-complete identity checking; this gives a very first exampleof a "natural" infinite monoid with difficult identity checking.

报告题目二：Minimal monoids generating varieties with complex subvariety lattices

报告人：SergeyGusev高级研究员

报告摘要：A variety is finitely universal if its lattice of subvarieties contains an isomorphic copy of every finite lattice. We show that the 6-element Brandt monoid generates a finitely universal variety of monoids and, by the previous results, it is the smallest generator for a monoid variety with this property. It is also deduced that the join of two Cross varieties of monoids can be finitely universal. In particular, we exhibit a finitely universal variety of monoids with uncountably many subvarieties which is the join of two Cross varieties of monoids whose lattices of subvarieties are the 6-element and the 7-element chains, respectively.

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)，目前担任乌拉尔联邦大学代数与理论计算机科学研究所所长。2017年当选芬兰科学与文学院外籍院士，2019-2021年被德国研究基金遴选为Mercator教授。

Volkov教授在代数，自动机理论，字上的组合学，形式语言等重要研究方向上发表论文160余篇，他的文章并曾两次在CIAA会议获得最佳论文奖。他是Semigroup Forum执行主编，是International Journal of Algebra and Computation，the Journal of Automata, Languages and Combinatorics和Ural Mathematical Journal等国际期刊的编委。

SergeyGusev，俄罗斯乌拉尔联邦大学高级研究员，2019年获得乌拉尔联邦大学的数学博士学位，主要从事半群理论研究，先后在Bull. London Math. Soc.,Semigroup Forum等代数学领域的知名期刊上发表论文10余篇。

甘肃应用数学中心

甘肃省高校应用数学与复杂系统省级重点实验室

数学与统计学院

萃英学院

2023年11月9日