**Abstract:**

In characteristic zero, the Hopf algebra of quasisymmetric functions QSym is isomorphic to the *shuffle algebra of compositions* Sh, and isomorphisms between them can be specified via *shuffle bases* of QSym. We give characterizations of shuffle bases via the notions of characters and infinitesimal characters, and we establish a universal property for Sh that is analogous to the universal property of QSym as a combinatorial Hopf algebra described by Aguiar, Bergeron, and Sottile. We use these results to give general constructions of quasisymmetric power sums, a class of bases for QSym which are closely related to shuffle bases, and prove properties of some larger families of quasisymmetric power sums. (This is joint work with Ricky Liu.)

**Note: This talk begins with a pre-seminar (aimed at graduate students) at 3:30–4:00. The main talk starts at 4:10.**

**Join Zoom Meeting: https://washington.zoom.us/j/ 91547335974Meeting ID: 915 4733 5974**