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Probability, integrability, and conformal invariance: August 23 – September 10, 2021


Organized by:

Eldad Bettelheim (Hebrew University),

Ilya Gruzberg (Ohio State University),

HÃ¥kan Hedenmalm (KTH),

Alisa Knizel (University of Chicago),

Paul Wiegmann (Univ. of Chicago)

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. A special issue associated with the program is planned to be published in the journal Entropy with contributions from the program attendees.

8/26. 10:00 amUniversality for outliers in weakly confined Coulomb-type systemsAlon NishryAbstract
8/27. 10:00 amLoewner Dynamics for the Multiple SLE(0) Process
Tom AlbertsAbstract
8/31. 10:00 amGeometrical web modelsJesper JacobsenAbstract
9/1. 10:00 amCorrelation functions for unitary invariant ensembles and Hurwitz numbers
Tamara GravaAbstract
9/1. 1:00 pmMultinomial modelsRichard KenyonAbstract
9/2. 10:00 amThe CFTs of 2D geometrical modelsHubert SaleurAbstract
9/9. 10:00 amThe hydrodynamics of many-body integrable systemsBenjamin DoyonAbstract
9/10. 10:00 amMatrix bootstrap revisited
Vladimir KazakovAbstract