First Passage Percolation and Related Models

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The workshop First-Passage Percolation and Related Models will take place at the International Center for Theoretical Sciences in Bangalore, India, July 27-Aug 14, 2020. This workshop will be devoted to presenting the latest research progress on the first-passage percolation (FPP), a probabilistic model of random growth, and closely related models. This is currently an active research area in contemporary probability theory and has important connections to statistical physics. Part of the workshop will be devoted to training graduate students and early career researchers in those topics. This award will provide travel support for the US based participants in the workshop.In two dimensions, FPP is a model that is conjecturally in the KPZ universality class, which consists of several models describing surface growth processes. Models in the KPZ class are intimately related with random matrix theory, asymptotic representation theory and number theory. FPP and related models have also been studied by physicists as a model for polymers in a random medium or as model of magnetic interfaces, and by biologists as the Eden model of bacterial growth. Much progress has been made on a class of these relatives which are in some senses "exactly solvable" by the methods of integrable probability. However, even at the physics level of heuristic, these models are poorly understood outside of solvable special cases; for instance, there are hardly any results for dimensions larger than 2. Unlike other conferences on FPP-type models, the ICTS workshop will emphasize methods outside of the integrable or exactly solvable framework. By focusing on techniques beyond exact solvability, the workshop will unify participants around solving fundamental problems of interest to the broader scientific community. The workshop website is maintained at https://www.icts.res.in/program/FPP2020.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.