Dr Michael Faulkner

Biography

I'm an Assistant Professor in the Warwick Centre for Predictive Modelling. My academic career started as a PhD student at University College London and Ecole normale supérieure de Lyon from 2011 to 2015, under the co-supervision of Steve Bramwell and Peter Holdsworth. After a short postdoc and teaching position at Bristol Mathematics, I then moved to Bristol Physics in August 2017 after winning an EPSRC postdoctoral research fellowship. I was also a visiting scientist at Ecole normale supérieure (Paris) from September 2017 to October 2018, and won a Max Planck Institute research fellowship to visit the Max Planck Institute for the Physics of Complex Systems in Dresden in April 2018.

For more details, please visit:

• GitHub
• Google Scholar
• arXiv
• ORCiD
• My personal website

Research

My broad research field is computational statistical physics, where I specialise in:

• Emergent electrostatics, slow mixing (eg, broken symmetry) and correlated dynamics in systems that experience the Berezinskii-Kosterlitz-Thouless phase transition, eg, certain planar magnets, superfluids and superconductors.
• Molecular simulation in soft-matter physics, with a focus on electrostatics, high precision and numerical stability.
• Monte Carlo sampling algorithms in statistical physics and Bayesian computational statistics, with a particular interest in piecewise deterministic Markov processes such as event-chain Monte Carlo.

My key 🔑 scientific achievements split between these three interconnected specialisms:

Planar materials

• Discovered general symmetry breaking at the Berezinskii-Kosterlitz-Thouless (BKT) transition. This resolved the paradox of symmetry breaking being observed in many BKT experiments in spite of a predicted absence of spontaneous symmetry breaking. Examples include superconducting films of lanthanum strontium copper oxide (LSCO). The result provides a model for directional mixing (or memory) timescales in a wide array of experimental systems.
• Defined the above new concept — general symmetry breaking — which encompasses both spontaneous symmetry breaking and the experimental anomalies.
• Discovered topological ergodicity breaking at the BKT transition in the 2D lattice-field Coulomb liquid (with Steve Bramwell and Peter Holdsworth). This was cited as a possible explanation for strongly correlated dynamics at the superconducting transition in the LSCO film and proved to induce the above general symmetry breaking.
• Developed the grand-canonical analogue of the Maggs lattice-field model of Coulomb liquids and showed its equivalence to the Villain model of planar magnets (see Section II and Appendix B of the paper on topological ergodicity breaking). We then…
• …presented an electric-field representation of the harmonic XY model — a more realistic model of planar magnets, superfluids and superconductors — which mapped the topological nonergodicity to the ergodic exclusion of global phase twists in the magnetic spins / condensate wavefunction.
• Collated and expanded on the above concepts. This elucidated fully the intimate connection between the topological order and broken U(1) symmetry at the BKT transition.

Molecular simulation and event-chain Monte Carlo

• Designed an event-chain algorithm for numerically stable all-atom molecular Coulomb simulations in soft matter (with Liang Qin, Tony Maggs and Werner Krauth). This is the only molecular simulation algorithm that mixes (equilibrates from a random initial configuration) Coulomb-based models in O(N log(N)) computations, where N is the number of particles. It also achieves machine precision and is the basis of…
• …our mediator-based Python-C application JeLLyFysh, which we set out in detail here with Philipp Höllmer.

• Event-chain Monte Carlo is a piecewise deterministic Markov process (PDMP). PDMPs mix at least as fast (typically much faster) than the diffusive dynamics of Metropolis Monte Carlo, and also guarantee numerical stability, unlike molecular-dynamics simulations. JeLLyFysh therefore holds much promise for the simulation of electrically charged Coulomb systems.

Sampling algorithms and interface with Bayesian computational statistics

• Presented an in-depth paper on statistical physics and its sampling algorithms, but in the language of statistics and machine learning (with statistician Sam Livingstone). We took a particular interest in phase transitions and event-chain Monte Carlo, presenting the latter in the language of PDMPs in Bayesian computation. This project used super-aLby and xy-type-models to simulate the models presented. We are now using our framework to explore correlated dynamics at phase transitions across statistical science — as we identified analogies with the emergent planar Coulomb liquid described above.
• Designed super-relativistic Monte Carlo for high-stability simulation of probability models in Bayesian computation (with statisticians Sam Livingstone and Gareth Roberts — see section 5.2 of the linked paper for details). By slowing down the Newtonian dynamics in high-gradient regions of probability space, this new simulation algorithm circumvents the numerical instabilities of Hamiltonian Monte Carlo when applied to light-tailed probability distributions. It also achieves machine precision and is the basis of our Python application super-aLby.

Teaching

My teaching focuses on the new MSc course Predictive Modelling and Scientific Computing, where I am co-lecturer of ES98D Particle-based modelling and supervisor/examiner of both group and individual projects. In 2023-24, I also provided a guest lecture on advanced simulation algorithms for ES98E Scientific Machine Learning.

I also provide weekly maths support to my first-year tutees and am co-lecturer for the third-year module ES386 Dynamics of Vibrating Systems.

Selected publications

Projects and grants

Software packages

Vacancies

I have a HetSys PhD project advertised for 2026-27 entry. The project will develop advanced Monte Carlo simulation algorithms for simulating models of glasses and complex materials, with longer term applications ranging from optical fibres to novel pharmaceutical formulations.

Informal enquiries to michael DOT faulkner AT warwick DOT ac DOT uk are welcome.