Advances in Probability: Integrability, Universality and Beyond

Since its discovery over two hundred years ago, the Gaussian distribution has come to represent one of mathematics greatest societal contributions – a robust theory explaining and analyzing much of the randomness inherent in the physical world. However, not all systems are well described by Gaussian theory. For example, classical extreme value statistics or Poisson statistics better capture the randomness and severity of events ranging from natural disasters to emergency room visits. 

Recently, significant research efforts have been focused on understanding systems which are not well described in terms of any of the classically developed statistical universality classes. The failure of these systems to conform with classical descriptions is generally due to the non-linear relationship between natural observables and underlying sources of random inputs and noise. The integrability (or exact solvability) of a few key models for these systems allows for detailed descriptions of new scaling limits and statistics, while universality results prove that these limiting behaviors are robust with respect to changing some of the underlying details of the models. 

This workshop will bring together experts at the forefront of recent advances in the probabilistic study of complex random systems and aims to probe the interplay between newly developed methods of integrability and universality in relation to these systems.

The workshop will focus on the following topics:

• Random interface growth, particle systems, stochastic PDEs, and the Kardar-Parisi-Zhang equation and universality class
• Random matrix theory
• Two-dimensional equilibrium statistical mechanics such as the Ising model, percolation, quantum Liouville gravity, and its relation to the Schramm Loewner evolution
• Logarithmically correlated processes such as Gaussian free field, and branching diffusion processes

Speakers:  Gerard Ben Arous (NYU), Nathanael Berestycki (Cambridge), Alexei Borodin (MIT), Amir Dembo (Stanford), Christina Goldschmidt (Oxford), Geoffrey Grimmett (Cambridge), Alice Guionnet (MIT), Grégory Miermont (ENS Lyon), Jason Miller (MIT), Ashkan Nikeghbali (Zurich), Neil O'Connell (Warwick), Yuval Peres (Microsoft), Jeremy Quastel (Toronto), Fabio Toninelli (Lyon), Craig Tracy (UC Davis), Vincent Vargas (Paris), Ofer Zeitouni (Weizmann, NYU)