October 7th, 2011, 9:30, CRM
  Joachim Kock:

  Symmetries of graphs and trees

  In quantum field theory, trees serve to express nestings of
  Feynman graphs.  Important aspects of the combinatorics of
  renormalisation are captured nicely by the Connes-Kreimer Hopf
  algebra of rooted trees.  However, the isolated graphs do not
  have a physical meaning: the meaning is carried rather by the
  Green functions, which are sums of graphs weighted by their
  symmetry factors.  Now the trees of Connes and Kreimer do not
  capture anything about symmetries of graphs.  I will explain
  how this can be 'fixed' by using instead operadic trees, or
  more precisely P-trees for certain polynomial endofunctors P
  defined over groupoids.