Konferenz: Symposium on Mathematical Physics

Vortrag von Dr. Victoria Lebed

Datum: 10.11.14 Zeit: 14.00 - 15.00 Raum: Y27H28

The Yang-Baxter equation (YBE) is omnipresent in modern physics and mathematics. Its realm includes statistical mechanics, quantum field theory, differential equations, quantum group theory, low-dimensional topology. In this talk we will present two new avatars of the YBE, bringing to light its unifying roles in algebra and in algebraic homology. Firstly, we will interpret associativity, Leibniz identity, self-distributivity, and some other recurrent algebraic identities as particular cases of the YBE, and discuss representation- and knot-theoretic applications of this interpretation. Secondly, we will present a homology theory for solutions to the YBE. It generalizes several familiar homology theories, and serves as a guideline for developing new ones, which we will see on an example arising in handlebody-knot theory. Our constructions are of a diagrammatic nature, which considerably simplifies technical calculations, common in homology.