Generalized permutahedra are a beautiful family of polytopes with a rich combinatorial structure. We explore the Hopf algebraic structure of this family. We then use this structure to unify old results, prove new results, and answer open questions about many objects of interest, such as graphs, matroids, posets, trees, set partitions, building sets, hypergraphs, and simplicial complexes. In particular, we shed new light on the basic problem of inverting a power series.

The talk will be based on joint work with Marcelo Aguiar, and will assume no previous knowledge of Hopf algebras or generalized permutahedra. Speaker(s): Federico Ardila (San Francisco State U.)