Published on *Max-Planck-Institut für Mathematik* (http://www.mpim-bonn.mpg.de)

Posted in

- Vortrag [1]

Speaker:

Andrew Tonks
Zugehörigkeit:

University of Leicester
Datum:

Sam, 2016-03-19 13:45 - 14:45 The Hopf algebras of the title are the cobar contruction on a reduced simplicial set, with

its Hopf algebra structure discovered by Baues, the algebra of rooted forests of Connes

and Kreimer, and the algebra of multi zeta values of Goncharov. In this talk we present

an operadic (and essentially simplicial) construction that encompasses and unies all of

these examples, giving deeper insight into each of them. Indeed, any cooperad which

has a suitably compatible multiplication may be given a canonical (innitesimal) bialgebra

structure, which is a Hopf algebra under connectivity assumptions. Further, we can show

that any reasonable Feynman category gives rise to a Hopf algebra. [Report on joint work

with I Galvez-Carrillo and R Kaufmann]

**Links:**

[1] http://www.mpim-bonn.mpg.de/de/taxonomy/term/39

[2] http://www.mpim-bonn.mpg.de/de/node/3444

[3] http://www.mpim-bonn.mpg.de/de/node/6477