Finding parking when not commuting

Abstract: Certain mathematical structures make a habit of reoccuring in
the most diverse list of settings. A list of examples might include the
catalan numbers, the quaternions, and the modular group. In this talk, I
will focus on a lesser known example which exhibits this intrusive type of
behavior: the non-crossing partition lattice. The talk will consist of a
gentle introduction to the lattice itself and three of its many guises: as
a way to count the parking functions defined by combinatorialists, as a
key part of the foundations of non-commutative probability, and as a
building block for a contractible space acted on by the braid groups.
Finally, as the talk is aimed primarily at non-specialists, all of the
areas listed above will be introduced as they arise.