Ferdinando Zanchetta (Università di Bologna)

Abstract: Algebraic structures on K-theory were instrumental for both the statement and the proof of many important results in algebra, topology and algebraic geometry (e.g. Hopf invariant one problem, Grothendieck-Riemann-Roch). However, their study into the context of higher algebraic K-theory proved to be more difficult and took decades to refine. After discussing some basic definitions and ideas, I will introduce the most recent techniques that have been developed to construct and understand algebraic structures on higher algebraic K-theory.