Department of Mathematics and Statistics

Department of Mathematics and Statistics
Department of Mathematics and Statistics

Geometry and Representation Theory Seminar


Monday, September 17th, 2018

Time: 4:30-5:30 p.m.  Place: Jeffery Hall 319

Speaker: Tianyuan Xu (Queen's University)

Title: Broken lines and the topological ordering of the alternating quiver of type A

Abstract:  The Positivity Conjecture in cluster algebra theory states that the coefficients of the Laurent expansion of any cluster variable in a cluster algebra are always positive integers. In 2014, Gross, Hacking, Keel and Kontsevich constructed a so-called Theta function basis to prove the conjecture for all cluster algebras of geometric type. A key ingredient in the construction of the Theta functions is the broken line model. In this talk, we will discuss the broken lines associated to the alternating quiver of type A, with an emphasis on relating its combinatorial properties to the topological ordering of the quiver, the partial order obtained by taking the transitive and reflexive losure of the relation “v<w if v->w is an edge” on the vertices of the quiver.

The talk is based work in progress with Ba Nguyen, David Wehlau and Imed Zaguia.