Integrable systems, growth processes and KPZ universality (12w5015)

Arriving in Banff, Alberta Sunday, September 23 and departing Friday September 28, 2012

Organizers

Estelle Basor (American Institute of Mathematics)

(Centre de recherches mathematiques, Universite de Montreal, and Concordia University)

Jeremy Quastel (University of Toronto)

(University of Wisconsin)

(University of California, Davis)

Objectives

The objective of this workshop is to bring together various experts in integrable systems, interacting particle systems and stochastic PDEs to allow the cross fertilization that will be necessary to go to the next level of universality theorems. Recent work of Amir, Corwin and Quastel and Sasamoto and Spohn have established a rigorous theory of the stochastic PDE called the KPZ equation. Their starting point is an exact formula by Tracy and Widom for the distribution of the particle position in the asymmetric simple exclusion process (ASEP). Extending these results to other initial conditions as well as the more difficult problem of general exclusion processes (not necessarily nearest neighbor) is currently an open problem. Recent experimental work by Takeuchi and Sano have established these processes occur in nature (see their recent Physical Review Letter).

A second aspect, and one that will be celebrated in the evenings, is the 80th birthday of Harold Widom (born September 23, 1932). Widom's work is at the core of many of these recent advancements.