Conference on Quantum Integrable Systems, Conformal Field Theories and Stochastic Processes

Columbia University, New York NY

Investigators

Abstract

This award will fund the conference "Quantum Integrable Systems, Conformal Field Theories and Stochastic Processes," which will be held from September 12-23, 2016, at the Institut d'Etudes Scientifique de Carges in Corsica, France. The conference website is https://indico.in2p3.fr/event/12461/. The topics of the conference are at the interface of mathematics and physics and are concerned with uncovering through exact calculation the universal behaviors of large, complex random systems. There are two main types of random systems -- those which are growing and those which have stabilized to a sort of equilibrium. The universal behaviors of each of these types of systems are rather different in characteristic. However, recent advances have indicated surprising connections between the behaviors of non-equilibrium and equilibrium systems. This conference will bring together experts in both areas with the aim of stimulating new advances and spark new connections. There is a strong emphasis on educating a new generation of researchers to appreciate and understand the broad cycle of ideas and motivations from both mathematics and physics in this area. Half of the lecturers will be mini-courses and the other half, research talks. This will benefit the many early-career researchers who will participate in the conference. The US participants funded by this award, most of whom are early-career researchers and graduate students, will benefit additionally by the opportunity to forge relations with their European colleagues. The organizers will actively encourage the participation of individuals from underrepresented groups in STEM, including women and minorities. 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 expected to be universal as well as the determination of which systems are meant 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 (KPZ) 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 partial differential equations 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.