Recent Progress in Two-Dimensional Statistical Mechanics (08w5084)


Richard Kenyon (Yale University)


How does ice form from water when its temperature cools? This and other natural phase transitions pose extremely difficult problems for mathematics. Recent work by Fields medalist Okounkov and Werner and their colleagues have shown the way to resolve, at least partially, some of the fundamental questions in two-dimensional phase transitions (related to such diverse questions as the spread of forest fires according to density of tree growth, spread of disease in a population distributed in two dimensions, or the shape of crystal surfaces at low temperature).

One of the goals of statistical mechanics is to understand the large-scale behavior of a system whose individual components are only interacting locally. While the real world of three dimensions is still far from understood, mathematical models for natural systems have in many cases been solved in two dimensions, and the solutions are often extremely deep, using tools from and yielding connections with many other parts of mathematics. In fact this is one of the qualities that mathematicians are very fond of: finding connections between hitherto disconnected areas of mathematics. The Banff International Research Station will host these mathematicians in its workshop "Recent Progress in Two-Dimensional Statistical Mechanics" on June 29 - July 04, 2008.

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 US National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnologí­a (CONACYT).