DMS Combinatorics Seminar

Time: Oct 18, 2022 (02:00 PM)
Location: ZOOM

Speaker: Andrea Jiménez (Instituto de Ingeniería Matemática Universidad de Valparaíso, Chile)
Title: Groundstates of the Ising Model on antiferromagnetic triangulations
Abstract: We discuss a dual version of a problem about perfect matchings in cubic graphs posed by Lovasz and Plummer. The dual version is formulated as follows "Every triangulation of an orientable surface has exponentially many groundstates'', where groundstates are the states at the lowest energy in the antiferromagnetic Ising Model.According to physicists, this dual formulation holds. In this talk, I show a counterexample to the dual formulation, a method to count groundstates which gives a better bound (for the original problem) on the class of Klee-graphs, the complexity of the related problems and, if time allows, some open problems. (This is joint work with Marcos Kiwi and Martin Loebl)