Loday's types of algebras and Rota's
types of operators
Abstract: After a quick overview of Loday's new "types of algebras", I will concentrate on the most recently defined "dendriform trialgebras" (there will be more scary names than this, but we will only be doing elementary algebra throughout). The free such trialgebra is based on the space of all rooted trees (Loday and Ronco). I will then describe several examples of trialgebras, all with a combinatorial flavor, and a general construction, which links trialgebras to one of Rota's favorite notions: Baxter operators. The punch line of the talk will involve quasi-symmetric functions, for a change.