报告一:Revisitation of the (matrix) partial orderings

报告时间：2023年4月12日（星期三）15:00-16:00

报告地点：Zomm 会议：860 4981 9861, PIN:888.

报告人：Oskar Baksalary教授

工作单位：波兰波兹南密茨凯维奇大学

举办单位：数学学院

报告人简介：Oskar Baksalary,波兰波兹南密茨凯维奇大学教授，研究领域为矩阵论及广义逆理论在物理中的应用，已在知名期刊上发表150余篇论文，目前担任IMAGE – The Bulletin of the International Linear AlgebraSociety，Electronic Journal of Linear Algebra期刊的编委。

报告简介：The talk provides anextensive investigation ofpartial orders.

报告二:Von Neumann regular rings and the realization problem

报告时间：2023年4月12日（星期三）16:00-17:00

报告地点：Zomm 会议：860 4981 9861, PIN:888.

报告人：Pere Ara教授

工作单位：西班牙巴塞罗那自治大学

举办单位：数学学院

报告人简介：Pere Ara,西班牙巴塞罗那自治大学教授，研究领域为环论、半群理论等，已在知名期刊Adv. Math., Trans. Amer. Math. Soc., Israel. J. Math., J. Algebra等杂志上发表100余篇论文，目前担任J. Algebra Appl.期刊的编委。

报告简介：I will survey several aspects of the realization problem for von Neumann regular rings, which asks whether any countable conical refinement monoid is isomorphic to the monoidV(R) of isomorphism classes of finitely generated projective modules over some von Neumann regular ringR. Various positive results have been obtained in recent years on this problem. In particular a recent result of Joan Bosa, Enrique Pardo and the presenter shows that every finitely generated conical refinement monoid is realizable by a von Neumann regularK-algebra, for an arbitrary fieldK. We say that a conical refinement monoidMistamein case it can be obtained as a direct limit of finitely generated conical refinement monoids. Otherwise, we say thatMis awild refinement monoid. It is expected that the above-mentioned result can be generalized to all countable tame refinement monoids. In joint work with Ken Goodearl, we explored the realization problem for a concrete wild refinement monoidN, which can be explicitly described in terms of generators and relations. It turns out that, for any fieldK, there is an exchangeK-algebraRsuch that

V(R)∼=N. TheK-algebraRis a universal localization of the semigroup algebra over the monogenic free inverse monoid. However, it turns out thatNcannot be realized by any von Neumann regular ring which is aK-algebra over anuncountablefieldK. Using a skew version of the construction mentioned before, we are able to realizeNas theV-monoid of a von Neumann regularK-algebra over any countable fieldK. This indicates that wild monoids behave in a quite different way to tame monoids in relation with the realization problem.

报告三:Hystorical notes on the Fuglede-Putnam theorem and three different proofs in the finite-dimensional case

报告时间：2023年4月12日（星期三）17:00-18:00

报告地点：Zomm 会议：860 4981 9861, PIN:888.

报告人：Dragana Cetkovic-Ilic教授

工作单位：塞尔维亚尼什大学

举办单位：数学学院

报告人简介：Dragana Cetkovic-Ilic，女，塞尔维亚尼什大学教授、博士生导师，2004年获得尼什大学博士学位，2010年获尼什大学终身教授，主要研究方向是算子广义逆理论及其应用。在Linear. Algebra. Appl.，Proc. Amer. Math. Soc.,Linear Multilinear Algebra，J. Austra. Math. Soc.，Acta Math. Sci.，Appl. Math. Comput.，J. Oper. Theory等杂志上发表高质量论文80余篇，2014年获得塞尔维亚数学会颁发的数学科学成就奖,现兼任Facta Universitatis, Filomat和Annals of Functional Analysis的编委和Acta Mathematica Hungarica, Mat. Vesnik, Publ. Inst. Math. Beograd, Filomat, J. Austra. Math. Soc.等多个高质量杂志的审稿人。现受聘为湖北师范大学“磁湖学者”讲座教授。

报告简介：In this talk, we provide three proofs forFuglede-Putnam theorem.