Fuglede's conjecture on the direct product of finite abelian groups

Abstract: We investigate Fuglede's conjecture on the direct product of abelian groups and its connection to the conjecture in $\mathbb{R}^n$ for $n\ge 2$. We overview the earlier results: Some important constructions will be shown, which disproves the conjecture in higher dimensions, and some techniques and ideas will be presented, which serves to prove the conjecture for certain abelian groups. Finally we will discuss some developments of the most recent directions of research. This talk is closely related to the talk of Gábor Somlai's about Fuglede's conjecture in the cyclic group and the one dimensional cases.

number theory

Audience: researchers in the discipline

Combinatorial and additive number theory (CANT 2022)