Ginevra Giordani

In this talk we will introduce the theory of polynomial identities in algebra. This is the research field in modern algebra studying algebraic structures that satisfy at least a non-trivial identity (PI-algebras), that arise via group theory and generalize the commutative world. After giving basic notions about identities in algebras and presenting the main classical results of this theory, we will look at PI-algebras with additional structures, mainly focusing on superalgebras with superinvolutions. Finally, we will present recent advances on central polynomials, that are an important tool in the study of polynomial identities.