Title: Constructions and nonexistence of formally dual pairs

Abstract: Formally dual subsets of finite abelian groups emerge as a combinatorial analogue of energy minimizing pairs of periodic configurations in Euclidean space. In this talk, we present known constructions via relative difference sets, generalized relative difference sets, and skew Hadimard difference sets, as well the concept of an even set, introduced by Li, Pott, and Schüler in 2019, which provides a restatement of a nonexistence conjecture for cyclic groups.