Mardi 24 Septembre


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Mardi 24 Septembre
Heure: 10:00 - 13:00
Lieu: Salle B107, bâtiment B, Université de Villetaneuse
Résumé: From PROs to combinatorial Hopf algebras
Description: Samuele Giraudo There is a well-known natural functorial construction which, from a set-operad, produces a Hopf algebra. We extend this construction to the category of PROs with some extra properties. By this generalization, we retrieve, among other, the Hopf algebra of noncommutative symmetric functions in various bases and the noncommutative Faà di Bruno Hopf algebra. We also obtain new ones, as some Hopf algebras involving forests, heaps of pieces, and some kinds of combinational circuits. All these Hopf algebras are similar in a sense to the Connes-Kremier Hopf algebra. In this talk, we shall recall some background about PROs, then present the construction associating a Hopf algebra with a PRO, and finally, review some examples of applications.
Heure: 10:00 - 13:00
Lieu: Salle B107, bâtiment B, Université de Villetaneuse
Résumé: Trees and graphs (from algebraic combinatorics to topology and random tensor models):
Description: Journées Math-STIC
Heure: 11:15 - 14:00
Lieu: Salle B107, bâtiment B, Université de Villetaneuse
Résumé: Kontsevich graph complexes
Description: Emily Burgunder Kontsevich proved that the Lie homology of symplectic Hamiltonians can be encoded as the homology of a Hopf bialgebra of graph complex attached to the commutative world. In this talk we will see some generalisation of this theorem : commutative world being replaced by operad, symplectic by a classical group, and we can consider Lie homology or its lifting to Leibniz homology.
Heure: 14:00 - 17:00
Lieu: Salle B107, bâtiment B, Université de Villetaneuse
Résumé: Action of the symmetric groups on the homology of the hypertree posets
Description: Bérénice Oger The set of hypertrees on n vertices can be endowed with a poset structure. This poset has been used by McCammond and Meier to study the group of motions of the trivial link, which is an analogue of the braid group. They also proved that this poset is Cohen-Macaulay and computed the dimension of its only homology group. After a short introduction on this topological context, we explain how we used the theory of species to compute the action of the symmetric group on this homology group. We then link it with the PreLie operad.
Heure: 15:15 - 18:00
Lieu: Salle B107, bâtiment B, Université de Villetaneuse
Résumé: Connes-Kreimer combinatorial Hopf algebra for the Ben Geloun-Rivasseau tensor field model
Description: Matti Raasakkar The Ben Geloun-Rivasseau quantum field theoretical model is the first tensor model shown to be perturbatively renormalizable. We define here an appropriate Hopf algebra describing the combinatorics of this new tensorial renormalization. The structure we propose is significantly different from the previously defined Connes-Kreimer combinatorial Hopf algebras due to the involved combinatorial and topological properties of the tensorial Feynman graphs. In particular, the 2- and 4-point function insertions must be defined to be non-trivial only if the superficial divergence degree of the associated Feynman integral is conserved.