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.