On Various Facets of Zero-Sum Invariants in Finite Groups

Zero-sum problems, rooted in additive combinatorics, explore conditions under which a sequence over a finite group contains a zero-sum subsequence with certain properties. Central to this area are group invariants such as the Davenport constant and the Erdős–Ginzburg–Ziv constant. Originally motivated by questions in non-unique factorization in number fields, these invariants remain difficult to determine even for finite abelian groups. In this talk, I will focus on recent developments in zero-sum problems over finite non-abelian groups, highlighting intriguing connections between the invariants of abelian and non-abelian structures.