报告时间： 2025年9月9日（周二）上午 9:30-10:30

报告地点：国交2号楼 315会议室

报告人：Prof. Mihalis Kolountzakis 克里特大学（Crete University）

摘要:  A fundamental domain $T$ of a group $H$ in a larger, abelian, group $G$ is a selection of one representative from each coset of $H$ in $G$. In other words $G=H\oplus T$ with the sum being direct. The main theme of this talk is when a collection $H_1, \ldots, H_n$ of subgroups of $G$, all of the same index, admit a common fundamental domain $T$

$$
H_1 \oplus T = H_2 \oplus T = \cdots = H_n \oplus T = G.
$$
In tiling language we are seeking a set $T \subseteq G$ that will tile $G$ when translated by any of the subgroups $H_1, \ldots, H_n$

This problem has many different aspects: analytic, geometric, combinatorial and purely algebraic. Perhaps the most well known of the versions of this problem is the Steinhaus Tiling Problem, which asks if there is a set $E \subseteq {\mathbb R}^2$ which tiles the plane when translated by any rotation of the lattice ${\mathbb Z}^2$.

We hope to be able to show several of these and explain some of the recent progress.