應(yīng)yl7703永利官網(wǎng)邀請，俄羅斯烏拉爾聯(lián)邦大學的 Mikhail Volkov 教授和 SergeyGusev 高級研究員將進行線下學術(shù)報告，歡迎全校師生參加。

報告時間：2023年11月10日(星期五)下午3:00

報告地點：理工樓631

報告題目一：Identities in twisted Brauer and twisted partition monoids

報告人：Mikhail Volkov教授

報告摘要：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.

報告題目二：Minimal monoids generating varieties with complex subvariety lattices

報告人：SergeyGusev高級研究員

報告摘要：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.

報告人簡介

Mikhail Volkov教授于1994年在圣彼得堡大學獲得俄羅斯國家博士學位(Doctor of Science degree in Mathematics)，目前擔任烏拉爾聯(lián)邦大學代數(shù)與理論計算機科學研究所所長。2017年當選芬蘭科學與文學院外籍院士，2019-2021年被德國研究基金遴選為Mercator教授。

Volkov教授在代數(shù)，自動機理論，字上的組合學，形式語言等重要研究方向上發(fā)表論文160余篇，他的文章并曾兩次在CIAA會議獲得最佳論文獎。他是Semigroup Forum執(zhí)行主編，是International Journal of Algebra and Computation，the Journal of Automata, Languages and Combinatorics和Ural Mathematical Journal等國際期刊的編委。

SergeyGusev，俄羅斯烏拉爾聯(lián)邦大學高級研究員，2019年獲得烏拉爾聯(lián)邦大學的數(shù)學博士學位，主要從事半群理論研究，先后在Bull. London Math. Soc.,Semigroup Forum等代數(shù)學領(lǐng)域的知名期刊上發(fā)表論文10余篇。

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2023年11月9日