Probability on Trees and Planar Graphs

The Banff International Research Station will host the "Probability on Trees and Planar Graphs" workshop from September 14th to September 19th, 2014.

The study of random processes on trees and planar graphs is a well established field of research at the core of probability theory, and one which has undergone tremendous growth in the past two decades. It is an extremely fertile subject area, with questions motivated by the most classical processes, such as random walks and percolation, on one hand, and by problems in statistical physics and computer science on the other. Much of the recent progress, including some substantial breakthroughs, derives from newly-discovered connections between probabilistic and geometric aspects of the objects studied. A key role is played by continuous and discrete conformal analysis, as well as related tools such as circle packings. Some of this work has been recognized by Fields medals in both 2006 (Werner) and 2010 (Smirnov), but the breakthroughs extend well beyond these works.

It is evident that geometric and analytic insights have a vital role to play in the study of random combinatorial structures, and that many fascinating conjectures and problems may now be within reach. The goal of this five day workshop is to connect researchers with backgrounds in probability, combinatorics, analysis and geometry in order to deepen our understanding of the interplay between these fields, and to explore the implications of geometric methods in probability.

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).

BIRS Scientific Director, Nassif Ghoussoub
E-mail: birs-director[@]birs.ca
http://www.birs.ca/~nassif