Quantum Integrable Systems, Conformal Field Theories and Stochastic Processes

Universality within and between complex random systems is a striking concept which has played a central role in the direction of research within probability, mathematical physics and statistical mechanics.  Complementary to universality, is the exact description of the behaviors that are supposed to be universal as well as the determination which systems are supposed to display them.  In recent years there has been an immense amount of progress in the rigorous mathematical understanding of certain universal scaling limits in both equilibrium and non-equilibrium statistical physical systems.  On the equilibrium side, critical scaling limits are often described in terms of conformal field theories, among which Liouville quantum gravity plays an important role.  On the non-equilibrium side, systems like growth processes are described through the Kardar-Parisi-Zhang universality class.

There is reason to believe that these two directions share many (as of yet) unexploited relationships.  For instance, the field of quantum integrable systems was developed to study equilibrium systems, but has now found itself center stage in the KPZ universality class.  Conversely, methods developed in stochastic PDEs for non-equilibrium systems have begun to make their way into constructive field theory.

The purpose of this two week conference is to bring together experts in these two areas and enable a lively exchange of ideas and methods through mini-courses and research talks.