Institut für Mathematik

Vortrag

Modul:   MAT075  Zurich Graduate Colloquium

What is.. a Drinfeld associator?

Vortrag von Ödül Tetik

Datum: 26.05.20   Zeit: 16.30 - 17.30   Raum: ABGESAGT

Drinfeld introduced his associators in the late 80's in his pioneering work on quantum groups. An associator in this original context is simply an assocativity isomorphism for comultiplication, needed to construct a certain kind of Hopf algebra, which is a type of quantum group. From the beginning, deep connections to topology (knot theory) and mathematical physics (conformal field theory) were explicit. It quickly became clear that associators are also tightly connected to an algebro-geometric object, the Grothendieck-Teichmüller group, conjectured to be isomorphic to the absolute Galois group of the rationals. Later, it was recognised that any associator gives a deformation quantisation of a Poisson manifold.

In this talk, I will introduce Drinfeld associators first in their original context, and then give a very simple and beautiful definition in terms of braids and chords, also defining the Grothendieck-Teichmüller group along the way. Then I will illustrate Drinfeld's original construction, explain how it falls out of conformal field theory, and wrap up with more on the connections to mathematical physics and topology.