Department of Mathematics

Seminar in Cluster algebras

  •  Matthew Mills, MSU
  •  Green sequences and local-acyclicity.
  •  09/20/2018
  •  3:00 PM - 4:00 PM
  •  C117 Wells Hall

In 2014 it was conjectured that the equality of the cluster algebra and upper cluster algebra is equivalent to the existence of a maximal green sequence. In this talk we will discuss a stronger result for cluster algebras from mutation-finite quivers with an emphasis on surface cluster algebras. Specifically we show that for all quivers from surface cluster algebras there exists a maximal green sequence if and only if the cluster algebra is equal to the cluster algebra if and only if the cluster algebra is locally-acyclic. We will also provide a counterexample to show that the result does not hold in general.



Department of Mathematics
Michigan State University
619 Red Cedar Road
C212 Wells Hall
East Lansing, MI 48824

Phone: (517) 353-0844
Fax: (517) 432-1562

College of Natural Science