Math Seminar Series
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Seminar in Cluster algebras more information...
Speaker: Nick Ovenhouse, U of Minnesota
Title: Laurent Expansion Formulas for Configurations of Flags
Time: 1:00 PM - 2:00 PM
Place: C204A Wells Hall
A cluster algebra can be associated to a polygon, where clusters correspond to triangulations of the polygon. These clusters give coordinates on the Grassmannian Gr(2,n). Schiffler gave explicit expressions for the cluster variables as Laurent polynomials, with the terms indexed by combinatorial objects called "T-paths". Fock and Goncharov defined a cluster algebra structure for the configuration space of tuples of flags in a 3-dimensional vector space, which generalizes the one given by triangulated polygons. In joint work with Andrew Claussen, we describe a suitable generalization of Schiffler's T-paths to this case, and show that the Laurent expansions of cluster variables are indexed by these generalized T-paths.