|Date: Friday, February 14, 2014
Location: 3866 East Hall (4:10 PM to 5:00 PM)
Title: Quiver mutation and Postnikov diagrams
Abstract: Postnikov diagrams are collections of oriented strands in the disc which satisfy an alternating condition and several minimality conditions. Postnikov diagrams come with a rule for `mutation' at certain faces, which produces a new Postnikov diagram. These diagrams and the mutations between them generalize several notable diagrammatic formalisms, such as wiring diagrams for permutations, urban renewal of bipartite graphs and domino tilings in the plane.
These diagrams can be studied by means of an associated quiver, in which mutation becomes quiver mutation (in the sense of cluster algebras). However, there are typically many more mutations of the quiver than of the original Postnikov diagram, which makes general statements about mutation-equivalent quivers difficult. In joint work with D. Speyer, we show how to use inequivalent Postnikov diagrams to study a larger portion of the mutation-equivalent quivers. The main consequence is that there is always a mutation-equivalent quiver with a source. This enables a purely combinatorial proof that any cluster algebra associated to one of these quivers is `locally acyclic'.
Speaker: Greg Muller
Institution: U. Michigan