From skew braces to the set-theoretic Yang-Baxter equation from affine viewpoint
In 2007 W. Rump discovered an interesting connection between algebraic structures, which he named braces, and the set-theoretic Yang-Baxter equation. During the talk, I will introduce the audience to skew braces, the generalisation of braces, and discuss their properties and links with the set-theoretic Yang-Baxter equation. Next, I will explain how by looking at them from a somehow affine point of view, we can notice new solutions. Then, I will reverse the process and start with a particular family of solutions of the set-theoretic equation and a group. I will construct a structure which resembles a skew brace, which will be called a near brace.