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Probability, integrability, and conformal invariance: August 16 – September 10, 2021

Organized by: Eldad Bettelheim, Ilya Gruzberg, HaĚŠkan Hedenmalm, Alisa Knizel, and Paul Wiegmann.

In recent years, the convergence of several topics in mathematics and physics have led to exciting developments in the study of fundamental problems in field theory, statistical mechanics, and probability theory. A deeper understanding has been gained of hidden symmetries associated with integrable structures and conformal invariance underlying and unifying different models and phenomena. Examples include conformal field theories and quantum Hall effects, and probabilists studying Schramm-Loewner evolutions, which led to spectacular results in two-dimensional statistical mechanics. More recently, these ideas have been extended to Liouville quantum gravity and Gaussian multiplicative chaos. Other developments are related to the renewed interest in inverse scattering and integrable systems in the context of the Ads/CFT. This interest has also led to developments in the area of non-equilibrium dynamics of exactly solvable systems and exact results in interacting particle systems such as asymmetric simple exclusion process and its generalizations. All these areas and subjects also have been linked with random matrices, an eternally beautiful and fruitful source of problems and ideas.

The program aims to bring together both mathematicians and physicists in order to discuss formal concepts that are fundamental to our understanding of solvable problems in statistical mechanics, field theory, and probability theory.