I am interested in solvable lattice models, an area of maths which offers exciting research possibilities in pure as well as applied mathematics. The study of solvable lattice models uses a variety of techniques, ranging from algebraic concepts such as Hecke algebras and quantum groups to analytic methods such as complex analysis and elliptic curves. Due to this wide variety of methods, the study of solvable lattice models often produces unexpected links between different areas of research. Currently I am studying such connections between stochastic processes, enumerative combinatorics & statistical mechanics on the one hand, and symmetric polynomials, algebraic geometry & representation theory on the other.
Aside from the pure maths aspects of solvable lattice models, they provide useful frameworks for modeling real world phenomena. Examples of solvable lattice models that are widely used in applications are stochastic processes, quantum spin chains and ladders as models for metals and superconductivity, random tilings as models for quasicrystals and exclusion processes as models for traffic and fluid flow.
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.
De Gier, J., Feher G. Z., Nienhuis B., & Rusaczonek M.
(2016). Integrable supersymmetric chain without particle conservation. Journal of Statistical Mechanics: Theory and Experiment. 2016(2), 23104. doi: 10.1088/1742-5468/2016/02/023104