The main focus of my research is to determine the set-theoretical solutions of the Yang-Baxter equation and the pentagon equation using appropriate algebraic structures, such as cycle sets, braces and their generalizations.
I am also interested to describe the regular subgroups of the affine group of a vector space.
Finally, one of my old interests, but always relevant to me, is the study of Lie’s properties of a ring.
My research activity focuses on the study of algebraic structures linked with solutions of the Yang-Baxter equation.
Postdoctoral Researcher
My research activity focuses on the study of the set-theoretical solutions of the Yang-Baxter equation introduced in [Drinfeld 1992] and their related algebraic structure (e.g. (semi)-braces, cycle sets, rack, etc.).
My current research activity is mainly focused on the determination of set-theoretical solutions of the Yang-Baxter equation and of the pentagon equation, two well-known equations of Mathematical Physics. My attention is particularly devoted to the study of algebraic structures strictly linked to these equations.
Marco Castelli
CV · list of publications
The main interest of my research is the study of cycle sets, non-associative algebraic structures related to the set-theoretic solutions of the Yang-Baxter equation.
Marzia Mazzotta
CV · list of publications
I graduated in Math in 2016 from the University of Salento. I am currently a PhD student working under the guidance of Prof. Francesco Catino at University of Salento. My research interests lie in the set-theoretical solutions of the pentagon equation.
