I have a wide range of possible projects to offer. See my research page, and feel free to email me if you have any questions, or would like more details. If you are interested in my research areas, then you should consider applying to MAC-MIGS; there is a ‘MAC-MIGS 2024’ programme for a September 2024 intake.
I am very much in favour of genuine co-supervision of PhD students. I have extensive experience of this, both with mathematicians and colleagues in applied science.
PhD student since 2022
email: O.O.Simeonov@sms.ed.ac.uk
Ogy is working on stochastic block models applied to debit-card transaction data with a view to providing intervention strategies to reduce carbon emissions. He is also interested in relative risks associated with detrimental behaviours.
PhD student since 2023
email: Jake.Skelton@ed.ac.uk
Jake is working on adaptive grids for pseudospectral methods, with a particular focus on applications in nonlocal and nonlinear PDEs. He is also interested more generally in applications of carefully-designed numerical domains.
PhD student since 2025
email: O.O.Simeonov@sms.ed.ac.uk
Yanpei is working on network-based approaches to modelling and policy formation for smoking. He is also interested in applications of techniques from statistical mechanics in these areas.
Postdoc, 2015-2017
Miguel was a postdoc joint with Serafim Kalliadasis and Greg Pavliotis (Imperial College London), working on our EPSRC funded grant ‘Statistical mechanics of soft matter: Derivation, analysis and implementation of dynamic density functional theories’. He was primarily working on dynamical density functional theory (DDFT) for anisotropic particles. In particular, he was focussing on the inclusion of inertia and hydrodynamic interactions in such models, which are crucial for describing a range of physical processes such as nucleation. He is then worked in the finance industry, primarily using stochastic models before co-founding Vortico, who focus on AI.
PhD student and Postdoc, 2015-2020
Rory did his PhD with me, jointly supervised by Jin Sun, with a thesis on ‘Analysis and applications of dynamic density functional theory’. He was particularly interested in modelling and computation for systems with short-range hydrodynamic interactions (lubrication forces). He also worked on the rigorous analysis, including existence and uniqueness, for DDFT-like equations, which was joint work with Greg Pavliotis (Imperial College London). After completing his PhD, he undertook a three-month Impact Acceleration Account Postdoc with WEST Beer on spectral element methods in the brewing industry. He then had a short postdoc position with Hartmut Löwen in Düsseldorf and now works in fluid dynamics modelling and engineering, currently as a software engineer at Edinburgh Designs.
PhD student, 2016-2020
Tim was a PhD student in the MIGSAA CDT. He did his first year extended project with me on non-adiabatic quantum molecular dynamics in two dimensions (joint with Volker Betz, Tübingen). He then went on to work on his thesis ‘Granular media at multiple scales: mathematical analysis, modelling and computation’, which was jointly supervised by Raffaella Ocone (Heriot-Watt, Engineering). Tim worked on the derivation and numerical implementation of dynamical density functional theory for granular media, and the rigorous derivation of the Boltzmann equation for inelastic particles (joint with Mark Wilkinson, Nottingham Trent). Tim then went on to become Chief Data Scientist at Brainnwave before co-founding Canongate AI.
PhD student, 2018-2022
Mildred was a PhD student in the MIGSAA CDT, jointly supervised by John Pearson. Her thesis was on a ‘Numerical framework for solving PDE-constrained optimization problems from multiscale particle dynamics’. Her first year extended project was on PDE-constrained optimization, in particular focusing on the inclusion of non-local terms, which are vital for many particle-based models, such as in complex fluids, opinion formation, or drone control. She extended this work through a combination of rigorous analysis and numerics. Mildred then moved on to work for The Hut Group as a software engineer before undertaking consultancy work.
PhD student and Postdoc, 2019-2023
Jonna was a PhD student in in the MIGSAA CDT, jointly supervised by John Pearson. Her thesis was on ‘Computational modelling and optimal control of interacting particle systems. Connecting dynamic density functional theory and PDE-constrained optimization’. She did her first year extended project on PDE-constrained optimization, in particular focusing on the inclusion of non-local terms, which are vital for many real-world particle-based models. She is then extended this work through a combination of rigorous analysis and numerics, with a particular focus on industrial applications. After passing her viva, she undertook a Maxwell Institute Research Fellowship, before moving on to work at RMS doing climate modelling.
PhD student, 2020-2023
Michael was a PhD student in the MAC-MIGS CDT, working with me and Adam Kirrander on non-adiabatic transitions in quantum molecular dynamics. His extended project focused on the use of a superadiabatic transition rate in the widely-used surface hopping algorithm. He then continued this work towards a number of mathematically-driven algorithms for quantum molecular dynamics. Michael is now an HPC Scientific Application Engineer at CINECA.
PhD student, 2019-2024
Adarsh was a PhD student based in Informatics with Valerio Restocchi. working on socio-economic complex systems. His thesis was on ‘Applications of agent-based models in tobacco control’, which included work that informs policy decisions to reduce the proliferation of smoking. He then undertook a postdoc at UCL developing computational tools to analyse ECHR cases. He is now a postdoc at Royal Holloway working on social norms and applications.
PhD student, 2020-2024
Iain was a PhD student in the MAC-MIGS CDT, working with me and Michela Ottobre on uniform in time averaging for SDEs. His thesis was on ‘Multiscale methods for stochastic differential equations and applications’. In particular, he was interested in deriving estimates for the averaging and homogensiation of multiscale (fast-slow) systems of interacting particles, for example determining when the averaged Fokker-Planck equation is a uniformly (in time) good estimate of the true dynamics. Iain is now an Innovation Research Associate at Warwick.
PhD student, 2021-2024
Katerina worked with Ben Leimkuhler, Toni Mey, James McDonagh at IBM Research, and me on machine learning for molecular dynamics. Her thesis was on ‘Higher-order damping mechanisms with applications in optimisation and machine Learning’.’ Katerina is now a senior research associate at Bristol.
PhD student, 2021-2025
Andrés was a PhD student in the MAC-MIGS CDT, jointly supervised by John Pearson and me. He worked on a range of constrained optimization problems, including PDE-Constrained Optimization for non-local, non-linear PDEs, such as those used in DDFT modelling, image processing, and phase separation in systems with singular kernels. He then went on to a postdoctoral position with John, continuing to work on efficient numerical schemes for optimal control.
