16-20 November 2020
IHES
Europe/Paris timezone

Tree-like Equations from the Connes-Kreimer Hopf Algebra and the Combinatorics of Chord Diagrams

20 Nov 2020, 15:15
30m
Marilyn and James Simons Conference Center (IHES)

Marilyn and James Simons Conference Center

IHES

35 route de Chartres, F-91440 Bures-sur-Yvette, France

Speaker

Lukas Nabergall (University of Waterloo)

Description

We describe how certain analytic Dyson-Schwinger equations and related tree-like equations arise from the universal property of the Connes-Kreimer Hopf algebra applied to Hopf subalgebras obtained from combinatorial Dyson-Schwinger equations in the work of Foissy. We then show how these equations can be solved as weighted generating functions of certain classes of chord diagrams and obtain an explicit formula counting some of these combinatorial objects.

Presentation Materials