|Date: Friday, September 11, 2015
Location: 4088 East Hall (3:10 PM to 4:00 PM)
Title: Lattice properties of oriented exchange graphs
Abstract: The exchange graph of a quiver is the graph whose vertices are mutation-equivalent quivers and whose edges correspond to mutations. The exchange graph admits a natural acyclic orientation called the oriented exchange graph, which is determined by fixing a particular quiver appearing in the exchange graph. The class of oriented exchange graphs contains interesting families of partially ordered sets such as the Tamari lattices and the Cambrian lattices introduced by Reading. In this talk, we will study oriented exchange graphs as partially ordered sets using quiver representations. We show that oriented exchange graphs with finitely many vertices are semidistributive lattices and that certain oriented exchange graphs with finitely many vertices are obtained by a lattice quotient of the lattice of biclosed subcategories, which we will introduce in this talk. The latter result generalizes Reading's Cambrian lattices in type A. No background on quivers and quiver representations will be assumed. This is joint work with Thomas McConville.
Speaker: Alexander Garver
Institution: U. Minnesota