Kamran graduated from the University of Warwick in July 2023 with an MMathPhys degree where he focused on functional analysis, PDEs and scientific computing. During his studies, he completed a summer research project looking at the rigorous derivation of the Boltzmann equation, and a master’s thesis studying convergence to equilibrium for a class of kinetic equations.  His other mathematical interests include numerical analysis and differential geometry. Outside of maths, Kamran enjoys cooking, hiking, reading and videogames.

Project title:
Approximation and variance reduction methods for stochastic partial differential equations

Supervisor(s):
Federico Cornalba, Tony Shardlow, James Foster

Project description:
Stochastic partial differential equations (SPDEs) are an ubiquitous modelling tool for spatiotemporal dynamics. Of particular interest are those arising from the study of interacting particle systems. Such systems are (i) computationally expensive to simulate at the individual particle level and (ii) typically fail to capture fluctuation behaviour at the ensemble level. By applying a coarse-graining procedure, one can instead study the evolution of the particle density via a continuous density-based model. Such models often take the form of SPDEs from the theory of fluctuating hydrodynamics, and in particular they should (i) be cheaper to simulate but (ii) be able to describe features of the particle model at the ensemble level. In this PhD we aim to tackle various problems related to the analysis, modelling and approximation of such SPDEs with a particular emphasis on applications in active matter.