** Speaker:** Bruce Sagan, Michigan State University

** Title:** Of antipodes and involutions

** Abstract: ** Let H be a graded, connected Hopf algebra. Then
Takeuchi's formula gives an expression for the antipode of H. But
this alternating sum usually has lots of cancellation. We will describe
a method using sign-reversing involutions to obtain cancellation-free
formulas for various H. This technique displays remarkable
similarities across the Hopf algebras to which it has been applied. No
background about Hopf algebras will be assumed. This is joint work
with Carolina Benedetti.