Marco Bonatto: A universal algebraic approach to Racks and quandles

Racks and quandles are binary algebraic structures arising in knot theory, representation theory of the braid groups and the study of Hopf algebras. The first part of the talk is an overview on quandle theory and the motivation behind it. In the second part of the talk we adapt the commutator theory developed by Freese and McKenzie for arbitrary algebraic structures to racks and quandles. The goal of such theory is to define the notions of abelian and central congruences, extending the familiar definitions in the setting of groups in order to talk about solvable and nilpotent objects.
For racks, the commutator theory has a nice and sharp interpretation in group theoretical language. We also provide some applications, both towards classification problems for finite quandles and knot theory.