Algebraic and Enumerative combinatorics seminar - Melissa Ulrika Sherman-Bennett-Dimer face polynomials in knot theory and cluster algebras

Abstract: The set of dimers (aka perfect matchings) of a connected bipartite plane graph G is a distributive lattice, as shown by Propp. The order relation on this lattice comes from the "height" of a dimer, which is a vector of nonnegative integers. In this talk, I'll focus on the dimer face polynomial of G, which is the height generating function of all dimers of G. This polynomial has close connections to knot invariants on the one hand, and cluster algebras on the other. I'll discuss joint work with Mészáros, Musiker and Vidinas in which we explore these connections. No knowledge of knot theory or cluster algebras will be assumed.

There will be a pre-seminar presenting relevant background at the beginning graduate level starting at 1:30pm.