Tuesday, May 2, 14:00, 7.527
Mikhail Gorsky (University of Vienna), A structural view of maximal
green sequences, I and II.
Maximal green sequences were first introduced by Keller in the studies of
connections between cluster algebras and quantum dilogarithm identities. The
talk concerns the structure of the set of all maximal green sequences of a
finite-dimensional algebra. There is a natural equivalence relation on this
set, which, as I will explain, can be interpreted in several different ways,
underscoring its significance. I will define several partial orders on the
equivalence classes of maximal green sequences, analogous to the partial
orders on silting complexes and generalizing higher Stasheff-Tamari orders
on triangulations of three-dimensional cyclic polytopes. We conjecture that
these partial orders are in fact equal, just as the orders in the silting
case have the same Hasse diagram. This can be seen as a refined and more
widely applicable version of the no-gap conjecture of Brüstle, Dupont, and
Perotin. I will sketch the proof of the conjecture for Nakayama algebras. If
time permits, I will also discuss two-dimensional higher Bruhat orders and
Cambrian maps in the context of posets of maximal green sequences.
The talk is based on joint work with Nicholas Williams (arXiv:2301.08681).