Title: Type A quivers and Schubert varieties
Abstract: An informal discussion on the topics in the title, relating to my GASC talk earlier in the week.
Title: Greedy Bases in Rank 2 Generalized Cluster Algebras
Abstract: Analogous to the inductive construction of cluster algebras, one can inductively define a generalized cluster algebra by replacing binomial exchange relations with polynomial exchange relations. We will discuss in this talk the rank 2 generalized cluster algebras associated to a pair of monic, palindromic polynomials. Our main result will be a combinatorial construction of a "greedy" basis in any such rank 2 generalized cluster algebra.
Title: Twist and Matchings
Abstract: In this talk, which is a report on joint work with R. Marsh, I will explain how to evaluate Laurent expansions for twisted Plücker coordinates with respect to any seed of the Grassmannian arising from a special class of planar networks called Postnikov diagrams. I will show how these expansions, which are predicted using the theory of cluster algebras, can be calculated using perfect matchings within a bipartite graph dual to the Postnikov diagram.
Title: Two Converse Theorems of Gorenstein Projective Modules
Title: The b-functions of quiver semi-invariants
Abstract: The main purpose of the talk is to explain how to compute the b-functions of quiver semi-invariants using reflection functors. After giving a quick background on b-functions (also called Bernstein-Sato polynomials) on prehomogeneous vector spaces, I will show by examples how one can compute the b-functions for quivers of tame type. Somewhat independently, I will also present a uniform rule on how to find the canonical decomposition for quivers of type D_n, if time permits.
Organized by Stephen Hermes, Dylan Rupel and Ryan Kinser.
Quivers and Invariant Theory Seminar for: Spring 2013, Fall 2012, 2011-2012 academic year
Back to Ryan's webpage.