On left nilpotent skew braces of class 2

In this talk, a detailed study of left nilpotent skew braces B of class 2 will be presented. We shall see that in the case that B is of nilpotent type, then it is centrally nilpotent; in particular, if B is of abelian type then it is right nilpotent of class 3. This opens the door to know much more about the inner structure of left nilpotent skew braces of class 2 and its associated solution of the Yang-Baxter equation. In the abelian type case, we shall delve into the description of these finitely generated braces.