Quantum Field Theory has become a universal language to study complex physical systems that involve many scales. Examples range from high energy physics to phase transitions and the turbulent motion of fluids. Mathematically these problems require statistical methods.The first topic in this project addresses problems in two dimensional Quantum Field Theory which give rise to the mathematical theory of random surfaces. Random surfaces reflect structures found in nature for which individual instances are all different but share common statistical properties. In the second part of the project we study the time evolution of non equilibrium systems that involve many scales. These are modelled by the mathematical theory of Stochastic partial differential equations.

2021

2025