Schedule

Spinny pictures and alternating sign matrices
Speaker: Jessica Striker

Abstract: We will discuss several ways to turn my favorite combinatorial objects, alternating sign matrices, into spinny pictures. We’ll also see how they arise in an algebraic context.

The wonderful world of snake graphs
Speaker: Esther Banaian

Abstract: We first review the construction of a snake graph, which gives an expansion formula for cluster variables in a cluster algebra of surface type. Then, we list some neat results relating to these graphs, including an enumeration formula and a connection to the representation theory of finite dimensional algebras. Time-permitting, we will discuss several related families of graphs and analogous results for each. No familiarity with cluster algebras will be necessary or assumed for the talk.

Snake Graphs for Graph LP Algebras
Speaker: Elizabeth Kelley

Abstract: LP algebras, introduced by Lam and Pylyavskyy, are a generalization of cluster algebras. These algebras are known to exhibit the Laurent phenomenon, but positivity remains conjectural in general. Graph LP algebras are finite LP algebras that can be encoded by a graph. For the subclass of graph LP algebras defined by trees, we define a type of vertex subset that we call weakly rooted. We give a combinatorial expansion formula for these sets in terms of maximally nested clusters using a generalization of snake graphs. (This is joint work with Esther Banaian, Sunita Chepuri, and Sylvester W. Zhang)