Random Growth Models and KPZ Universality (21w5175)

Organizers

Ivan Corwin (Columbia University)

Jeremy Quastel (University of Toronto)

(University of Utah)

(University of Wisconsin - Madison)

Description

The Banff International Research Station will host the "Random Growth Models and KPZ Universality" workshop in Banff from STARTDATE to ENDDATE.


Irregular growth is a ubiquitous phenomenon in nature, from the growth of tumors, crystals, and bacterial colonies to the propagation of forest fires and the spread of water through a porous medium. Mathematical models of random growth have been a driving force in probability theory over the last sixty years and a rich source of important ideas. The analysis of random growth models began in the early 1960s with the introduction of the Eden model by Eden and first-passage percolation by Hammersley and Welsh. The field witnessed several breakthroughs in the 1980s and 1990s, from the introduction of more random growth models, including the Kardar, Parisi, and Zhang (KPZ) equation and the KPZ universality class, to the ground-breaking works of Tracy and Widom and of Baik, Deift, and Johansson, and the seminal works of Newman and coauthors. These results caused a flurry of activity and more analytical and geometrical tools were developed.     

The study of random growth models connects to a large number of areas in probability theory such as integrable probability, homogenization, percolation, disordered systems, interacting particle systems, random matrices, SPDEs, random polymer measures, random dynamical systems, and random walk in random environment. The last two decades have seen rapid advances in all these directions, with a significant acceleration in progress in several of these subfields recently, including solutions of several long-open problems. This is an exciting time for the subject, with new possibilities in extending universality, new geometric approaches, and more. The main objective of this workshop will be to bring together a number of top experts on these various subfields to disseminate these recent developments and exchange ideas that will fertilize the ground for yet another leap forward. This opportunity will also be used to celebrate the work of Timo Sepp\"al\"ainen in the field on the occasion of his 60th birthday.


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).