Fundamental models of interacting particles, such as those occurring in mathematical physics and queuing theory, are widely studied to understand non-equilibrium behavior in physical systems consisting of large numbers of particles, to study large classes of transport phenomena, scheduling mechanisms and interface growth.
The mathematics of quantum toroidal algebras is remarkably rich, and so are their applications to physics. These algebras and their representation theory arise in the mathematics of high-energy physics, string theory and supersymmetric gauge theories. They also play an important role in the analysis of central models in condensed matter physics, stochastic interacting particle systems and integrable probability. ACEMS researchers contribute to quantum toroidal algebras, which are quantum versions of toroidal Lie algebras.