报告地点：腾讯会议：69744317

报告人：Xavier Mary 教授

工作单位：Université Paris-Ouest Nanterre – La Défense

举办单位：数学学院

报告人简介：Xavier Mary, 2006年博士毕业于巴黎大学。目前为法国巴黎第十大学教授，主要研究领域包括：半群理论、环论、代数等。X. Mary教授在国际代数领域享有很高的知名度，于2011年引入了“The inverse along an element”,现称之为Mary逆，被广泛的研究。目前国际上以Mary逆命名此逆。目前，X. Mary教授已在Linear Algebra Appl., Linear Multilinear Algebra, Appl. Math. Comput., Comm. Algebra J. Algebra Appl.等杂志上发表了30篇学术论文。并且，X. Mary教授主持过欧洲地平线2020项目。

报告1：On an equivalence between semigroups and certain categories with thin strict factorization systems-1

报告时间：2024年4月24日（星期三）15:30-16:30

报告简介：Since the seminal work of Nambooripad, there has been a growing interest in representations of semigroups by certain small categories. This led to the well-known equivalence between inverse semigroups and inductive groupoids (the Ehresmann-Schein-Nambooripad theorem), or the less-known equivalences between the category of regular semigroups, the category of regular inductive groupoids, and the category of cross-connections. In the talk, we will show how the Schützenberger category of a semigroup allows the construction of an equivalence between the category of semigroups and the category of small categories with a strict factorization system and a bimodule map. Taking natural transformations into account, this extends to an equivalence for a 2-category of unital semigroups. As an application, we will show that in this 2-categorical setting, 2-equivalence happens to be exactly Morita equivalence (of monoids).

报告2：On an equivalence between semigroups and certain categories with thin strict factorization systems-2

报告时间：2024年4月26日（星期五）15:30-16:30

报告简介：Since the seminal work of Nambooripad, there has been a growing interest in representations of semigroups by certain small categories. This led to the well-known equivalence between inverse semigroups and inductive groupoids (the Ehresmann-Schein-Nambooripad theorem), or the less-known equivalences between the category of regular semigroups, the category of regular inductive groupoids, and the category of cross-connections. In the talk, we will show how the Schützenberger category of a semigroup allows the construction of an equivalence between the category of semigroups and the category of small categories with a strict factorization system and a bimodule map. Taking natural transformations into account, this extends to an equivalence for a 2-category of unital semigroups. As an application, we will show that in this 2-categorical setting, 2-equivalence happens to be exactly Morita equivalence (of monoids).

报告3：Characterizations of clean elements-1

报告时间：2024年4月28日（星期日）15:30-16:30

报告简介：We characterize clean elements in unital and general rings by means of outer inverses. Some special cases, such as both clean and unit-regular elements, or strongly clean elements, are discussed. As an application, we also derive new characterizations of strongly regular elements.

报告4：Characterizations of clean elements-2

报告时间：2024年4月29日（星期一）15:30-16:30

报告简介：We characterize clean elements in unital and general rings by means of outer inverses. Some special cases, such as both clean and unit-regular elements, or strongly clean elements, are discussed. As an application, we also derive new characterizations of strongly regular elements.