Dimers, Ising Model, and their Interactions (19w5062)


Gourab Ray (University of Victoria)

Julien Dubedat (Columbia University)

Hugo Duminil-Copin (Institut des Hautes Études Scientifiques (IHÉS))


The Banff International Research Station will host the "Dimers, Ising Model, and their Interactions" workshop in Banff from November 17, 2019 to November 22, 2019.

Statistical physics models on graphs have been one of the most exciting area of research in probability theory over the past few decades. Since the 80's, physicists have predicted that in two dimensions such models exhibit many beautiful large scale conformal symmetries. At criticality the behaviour of such models is governed by certain random self similar fractals. Rapid progress in this area has been made specially in the last decade with the introduction of Schramm-Loewner evolution and the development of discrete conformal analysis. Two fields medals have been awarded (Smirnov, 2006 and Werner, 2010), recognizing the achievements in this area.

In this workshop we propose to focus on a particularly popular model called the dimer model and its connections with other statistical physics models, especially the Ising model. The dimer model can be simply defined as a model of perfect matching, and it is well-established that this model stands at an interface of geometry, combinatorics, algebra and analysis. The Ising model is perhaps one of the most classical models of statistical physics and it can be used to describe the behaviour of a magnet at various temperatures. Deep and fascinating mathematics describe the behaviour of these two models and their interconnections. With all the recent exciting developments many longstanding open problems (such as the convergence of double dimer interfaces) seem within reach.

The goal of this workshop is to bring together researchers with expertise in various aspects of this field so that we can have a better understanding of the interplay between these various branches of mathematics, which forms the core of this subject of research.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT).