Dimers and Geometry

05/03/2016 - 15:30
05/03/2016 - 16:30
Richard Kenyon, Brown University
Seminar Physique Mathématique CRM, UdeM, Pavillon André-Aisenstadt, 2920, ch. de la Tour, salle 4336

 The Kasteleyn matrix (whose determinant enumerates dimer covers of a planar graph) has a geometric interpretation as the differential of a certain mapping involving planar tilings. This observation has several topological consequences, for example one can show that the space of convex embeddings (embeddings with convex faces) in R^2 of a planar graph with pinned boundary is homeomorphic to a ball. We discuss this and similar topological results, as well as results on random embeddings and their limit shapes, and underlying integrable structures.

Last edited by on Fri, 04/29/2016 - 16:31