Title: A Gentle Introduction to the Drinfel'd Associator
Speaker: Martin Bordemann
Institution: Université de Haute Alsace, Mulhouse, France
Date & Time: April 11, 2024, 20:00–22:00
Location: Zoom ID: 904 645 6677, Password: 2024
This pedagogical talk introduces the renowned
Drinfel'd associator, invented by V.G. Drinfel'd in 1989/90, and provides a proof of its hexagon and pentagon identities. The associator is fundamental in quantizing (quasi) Lie bialgebras (e.g., works by P.I. Etingof–D.A. Kazhdan and B. Enriquez–G. Halbout), deformation quantization (D.E. Tamarkin), and number theory (via multiple zeta values), as it encodes the deformation of symmetric monoidal categories into braided ones using an "infinitesimal braiding."
While Drinfel'd’s original exposition (and most textbook treatments) are highly condensed, often requiring prerequisites in complex analysis, algebraic topology, or conformal field theory, this talk offers a more elementary approach. We use limits of (formal) parallel transports along explicit paths in star-shaped domains of the real line and plane, relying on flat (formal) connections derived from the Knizhnik-Zamolodchikov connection. This method avoids excessive technicality, making the associator’s construction and properties accessible to a broader audience.
Martin Bordemann has been a Full Professor in the Mathematics Department at the Université de Haute Alsace, Mulhouse, France, since 2000. He earned a PhD in mathematical physics (1990, under Hartmann Römer, Freiburg, Germany) studying integrable systems and a Master’s in Mathematics (1989, under Otto Kegel, Freiburg) on metrized Lie algebras.
His research focuses on
deformation quantization and algebraic deformation theory, with contributions to the geometric and algebraic foundations of quantum mechanics and noncommutative geometry. He has published extensively on topics such as the Fedosov quantization method, Poisson geometry, and the interplay between classical and quantum structures.
