I am currently a supervisor for the MAC-MIGS CDT (Maxwell Institute Graduate School Centre for Doctoral Training in Modelling, Analysis, and Computation). PhDs in MAC-MIGS are four years, with the first year devoted primarily to training (i.e. further study), group work, and an extended project (which normally leads into a PhD). Note that MAC-MIGS students do not choose their supervisor on arrival, but rather have a chance to meet potential supervisors and make an informed decision about which projects they are interested in.
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.
PhD student since 2019
email: A.Prabhakaran@sms.ed.ac.uk
Adarsh is based in Informatics with Valerio, and is working on socio-economic complex systems. In particular, he is studying models for the proliferation of smoking, based on models from mathematical biology and sociology, including parameters derived from real-world studies.
PhD student since 2020
email: is79@hw.ac.uk
Iain is working on uniform in time averaging for SDEs. In particular, he is 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.
PhD student since 2021
email: A.Karoni-1@sms.ed.ac.uk
Katerina is working with us, James McDonagh at IBM Research, and Toni Mey (UoE, Chemistry) on machine learning for molecular dynamics. She is currently studying symmetry-preservation in machine-learned force fields and related questions.
PhD student since 2021
email: Aandres.miniguano-trujillo@ed.ac.uk
Andrés is working on a range of constrained optimization problems, including PDE-Constrained Optimization for non-local, non-linear PDEs, such as those used in DDFT modelling.
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.
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 now working in the finance industry, primarily using stochastic models.
PhD student and Postdoc, 2015-2020
Rory did his PhD with me, jointly supervised by Jin Sun, 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 undertook a postdoc position with Hartmut Löwen in Düsseldorf and now works in fluid dynamics modelling and engineering.
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 is now a Data Scientist at Brainnwave.
PhD student, 2018-2022
Mildred was a PhD student in the MIGSAA CDT, jointly supervised by John Pearson, and worked 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. She passed her viva in October 2022 and now works at The Hut Group.
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 now extending this work through a combination of rigorous analysis and numerics, with a particular focus on industrial applications. She passed her viva in November 2022. She then undertook a Maxwell Institute Research Fellowship, before moving on to work in industry 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.
