A survey on maximal green sequences

Source abstract

Maximal green sequences appear in the study of Fomin–Zelevinsky’s cluster algebras. They are useful for computing refined Donaldson–Thomas invariants, constructing twist automorphisms and proving the existence of theta bases and generic bases. We survey recent progress on their existence and properties and give a representation-theoretic proof of Greg Muller’s theorem stating that full subquivers inherit maximal green sequences. In the appendix, Laurent Demonet describes maximal chains of torsion classes in terms of bricks generalizing a theorem by Igusa.