The No Gap Conjecture for tame hereditary algebras
  The "No Gap Conjecture" of Br\"ustle-Dupont-P\'erotin states that the set of lengths of maximal green sequences for hereditary algebras over an algebraically closed field has no gaps. This follows from a stronger conjecture that any two maximal green sequences can be "polygonally deformed" into each other. We prove this stronger conjecture for all tame hereditary algebras over any field. 
Stephen Hermes and Kiyoshi Igusa
math.RT