Department of Mathematics - Seminar on Pure Mathematics - Interpolation of Hopf monoids

In this talk we lift the theory of r-quasisymmetric functions to the theory of Hopf monoids. We provide a general method of interpolating between two Hopf monoids, one being the free monoid on a positive comonoid and the other being the free commutative monoid on a positive comonoid. We then apply this interpolation to a few examples including planar rooted forests and parking functions.