06.11.2024, 14:00 - 16:00
– Campus Golm, Building 9, Room 2.22 and via Zoom
Institutskolloquium
Graphon Models for Inhomogeneous Random Graphs
Olga Klopp (Paris), Nicolas Verzelen (Montpellier)
Lucas Delage (Potsdam)
It is well known that the grafting operator B_+, defined on the vector space of forest by gluing every tree of a forest to a common root, obeys the following universal property : for any commutative Hopf algebra H, and any endomorphism L of this Hopf algebra such that \Delta \circ L = L \otimes 1 + (Id \otimes L) \circ \Delta (with \Delta the coproduct of H), then there is a unique morphism of Hopf algebra \rho from the Connes Kreimer Hopf algebra to H such that L \circ \rho = \rho \circ B_+. Furthermore It was shown that one can define a Pre Lie algebra on rooted trees which is isomoprhic to the free Pre Lie Algebra. We will inspect the link between these two universal property.