主 讲 人 ：Alfred Geroldinger    教授

活动时间：2025-11-07 15:00:00

地      点 ：数学科学学院D203报告厅 ZOOM: - link: https://us06web.zoom.us/j/86763384947?pwd=qXhOzOcHvaaiw2jqADI8iqNavdgm14.1 （ID: 86763384947； passcode: 612593）

主办单位：数学科学学院

讲座内容：

Let $G$ be an additive abelian group and let $\Gamma \subseteq \mathbb Z$ be a subset. A sequence $S = (g_1, \ldots, g_{\ell}$ of terms from $G$ is a $\Gamma$-weighted zero-sum sequence if there are $\gamma_1, \ldots, \gamma_{\ell} \in \Gamma$ such that $\gamma_1 g_1 + \ldots + \gamma_{\ell} g_{\ell} = 0$. Apart from the fundamental case when $\Gamma = \{1\}$, one of the most studied cases is when $\Gamma = \{\pm 1\}$.

Weighted zero-sum problems have been investigated in the literature for roughly twenty years. Fresh impetus has come from connections to algebraic problems arising in Ring Theory and Factorization Theory. We will highlight these connections and consider algebraic and arithmetic properties of the monoid $\mathcal B_{\Gamma}(G)$ of all $\Gamma$-weighted zero-sum sequences over $G$.

主讲人介绍：

Alfred Geroldinger received a Master Degree in Mathematics from the University of Vienna, a Master Degree in Computer Science from the Vienna University of Technology, and a PhD in Mathematics from the University of Graz. He is a member of the Graz School of Discrete Mathematics and a professor at the University of Graz. To date, he has authored/coauthored 130 research articles and coauthored three books:

• Non-Unique Factorizations (with F. Halter-Koch), CRC Press, 2006.

• Combinatorial Number Theory and Additive Group Theory (with I. Ruzsa), Springer 2009.

• Combinatorial Factorization Theory (with D.J. Grynkiewicz and Q. Zhong), AMS Math. Surveys and Monographs, to appear.