Maximal Green Sequences for Type A Quivers

Maximal green sequences are certain mutation sequences of a framed quiver \widehat{Q}. Some applications of maximal green sequences include Reading's Cambrian lattices in combinatorics, computations of spectra of BPS states in physics, and quantum dilogarithm identities in representation theory. Maximal green sequences have been studied for many acyclic quivers by Br\"{u}stle, Dupont, and Pérotin, by Keller, and by Qiu. We present a method for constructing an explicit maximal green sequence of any type A quiver (i.e. a quiver that is mutation equivalent to an orientation of a type A Dynkin diagram). This is joint work with Gregg Musiker.