ERC Advanced Grant - 2015/2021 - IntRanSt - 669306

Title

Integrable Random Structures

Principal Investigator

Neil O'Connell

Summary

The aim of this project is to develop and study integrable / exactly solvable models in probability. Examples of such models include interacting particle systems, random polymers, random matrices and various combinatorial models related to the theory of symmetric functions and Young tableaux. A common theme is some underlying algebraic structure which accounts for the integrability of the model in question. The project has a strong emphasis on models of representation-theoretic origin, particularly in the context of the theory of Young tableaux and its vast generalisations. For example, there is a remarkable connection between a birational version of the celebrated Robinson-Schensted-Knuth correspondence and GL(N)-Whittaker functions; moreover, this connection may be applied to the study of a class of random polymer models which belong to the so-called KPZ universality class of random matrix theory. The resulting theory has been substantially developed within the context of this project, including extensions to models with additional symmetries and also non-commutative versions. Some other recent developments include: a new approach to the study of moments of random matrices, connections between random matrices and SLE, progress on random sorting networks, and scaling limits for Whittaker measures.

Team

Jonas Arista (Sep 2015 - Sep 2020)

Elia Bisi (July 2018 - Sep 2020)

Philip Cohen (PhD student, Sep 2017 -)

Fabio Deelan Cunden (Sep 2016 - Sep 2020)

Antoine Dahlqvist (Oct 2017 - Dec 2018)

Samuel Johnston (Oct 2017 - Sept 2019)

Jon Warren (Jan - Jun 2020)

Activities

Probability seminars

Workshop: Randomness and Symmetry, UCD, June 18-22, 2018

Workshop: Random Matrices and Integrable Systems, UCD, May 23, 2018

Introductory lectures on random matrices and free probability, UCD, November 10 - December 8, 2017