Torsion groups and the Bienvenu-Geroldinger conjecture
主 讲 人 ：Weihao Yan 博士
活动时间：03月19日17时00分
地 点 ：伟德bv1946D203报告厅（https://us06web.zoom.us/j/86763384947?pwd=qXhOzOcHvaaiw2jqADI8iqNavdgm14.1 ）
讲座内容：
Let $M$ be a monoid (written multiplicatively). Equipped with the operation of setwise multiplication induced by $M$ on its power set, the collection of all finite subsets of $M$ containing the identity element forms a monoid itself, denoted by $\mathcal P_{{\mathrm{fin}}, 1}(M)$ and called the reduced finitary power monoid of $M$.
This naturally leads to the question of whether, for all $H$ and $K$ in a given class of monoids, $\mathcal P_{\mathrm{fin},1}(H)$ and $\mathcal P_{\mathrm{fin},1}(K)$ are isomorphic if and only if $H$ and $K$ are.
The problem originates from a conjecture of Bienvenu and Geroldinger [Israel J. Math. 265} (2025), 867-900], which was quickly settled by Tringali and Yan in [Proc. AMS, 153 (2025), No. 3, 913-919]. In this talk, I will discuss how the problem has a positive solution in the case where $H$ and $K$ are both torsion groups.
主讲人介绍：
Weihao Yan is a first-year PhD student in the School of Mathematical Sciences at Hebei Normal University (HebNU), China. He is enrolled in the university's combined Master's–PhD program. During the Master's phase of his studies, he conducted research on power semigroups under the supervision of Salvatore Tringali (HebNU). He has published two papers on power semigroups, in the Proceedings of the American Mathematical Society and the Journal of Combinatorial Theory, Series A, with a third forthcoming in the Bulletin of the London Mathematical Society (pending final acceptance). Since June 2025, he has been working on geometric constructions of divisible design graphs and their applications to signed graphs under the supervision of Bart De Bruyn (Ghent University, Belgium) and Sergey Goryainov (HebNU).