A uniform bijection between
nonnesting and noncrossing partitions

In 2007, Dimitri I. Panyushev defined a remarkable map on the set of antichains in the root poset of a finite Weyl group. In this talk, I will present a uniformly described bijection between those antichains and elements in the noncrossing partition lattice. It identifies Panyushev's map with the Kreweras complement on noncrossing partitions. I will also show how this bijection can be used to prove several conjectures concerning the Panyushev map, and a cyclic sieving phenomenon conjectured by David Bessis and Vic Reiner. This is joint work with Drew Armstrong and Hugh Thomas.