Statistical physics studies discrete models with randomness, typically defined on a lattice. The goal is to understand the large scale behavior, in the scaling limit, as the number of constituents is taken to infinity while keeping the geometry fixed.
Two-dimensional models occupy a special place in the research, as their scaling limits often possess enough algebraic structure to make them mathematically tractable or even exactly solvable. The tradition in physics is to formulate the scaling limit as a quantum field theory with conformal symmetry, wheras recent mathematical research has focused on defining the limit in terms of for example random curves.
The objective of this research project is to reveal algebraic structures in stochastic lattice models and their random geometry description, and apply these structures to the study of the models and their scaling limits. |