Report Title：Skew Braces: Structure and Connections
Reporter：Lorenzo Stefanello
Affiliation: University of Pisa
Report Time:May 7, 2026, 13:00-15:00
Report Location:Zoom Id: 904 645 6677，Password: 2026
Meeting:https://us06web.zoom.us/j/9046456677?pwd=CWu8WvANi9ohJh4OW91sTVqBM9zsOT.1&omn=86972689584
Abstract:
Skew braces are algebraic structures equipped with two group operations interacting in a compatible way, and have attracted increasing attention due to their rich structure and connections with various areas of algebra. In this talk, we introduce skew braces through basic examples and discuss some of the motivations behind their study. We then focus on three main problems arising in this context. First, we investigate the relationship between the two group operations, including results related to a conjecture of Byott, classification results in specific cases, and connections with radical rings and problems concerning unit groups of rings. Second, we present results related to Hopf–Galois structures, illustrating how skew braces provide a natural framework for studying these objects and describing some recent developments. Finally, we introduce Rota–Baxter operators in this context, showing how they arise naturally from the problem of constructing skew braces, and examining the question of whether all skew braces can be obtained in this way.
Bio:
Lorenzo Stefanello is a mathematician whose research focuses on skew braces and their connections with Hopf–Galois theory. He earned a PhD in Mathematics from the University of Pisa, working at the intersection of abstract algebra and algebraic number theory.
