Speaker: Dr. Eshita Mazumdar from Ahmedabad University.
Date and Time: Friday, January 28, 2022, 11:00-12:00 via Zoom. Please contact Will Brian to obtain the Zoom link.
Title: Zero-sum problems
Abstract: Zero-sum problems are basically combinatorial in nature. It deals with the condition which ensures that a given sequence over a finite group has a zero-sum subsequence with some prescribed property. There are many invariants associated with zero-sum problems. One of such invariants is the Davenport Constant. The original motivation for introducing the Davenport Constant was to study the problem of non-unique factorization domain over number fields. The precise value of this group invariant for any finite abelian group is still unknown. In this talk I will discuss an extremal problem related to Weighted Davenport Constant and introduce several exciting combinatorial results for finite abelian groups. Also, characteristics of these constants on restricted sequences will be discussed. If time permits I will talk about an ongoing project where we introduced a new group invariant which is a natural generalization of the Davenport Constant.