Poisson brackets and flat connections /CANCELLED

par Prof. Anton Alexeev (Université de Genève)

vendredi 16 déc. 2022, 16:30 → 18:00 Europe/Paris

IHP salle 01

The seminar is cancelled (announced for the next year) 

because of the STRIKE of SNCF-Sud

A flat connection with regular singularities on a complex plane is characterized by its residues at singular points. A theorem of Hitchin establishes a surprizing link between the linear Kirillov-Kostant-Souriau (KKS)Poisson bracket on the residues and the Goldman bracket on traces of holonomies corresponding to closed loops. In this talk, we will show how to generalize this result to regularized holonomies corresponding to paths starting and ending at singular points. Our main technical tool is a version of the Drinfeld's pentagon equation suitable for paths with self-intersections.

 

The talk is based on a joint work in progress with Florian Naef and Muze Ren.