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.

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 supervise a group project and will also provide a guest lecture on advanced simulation algorithms in Spring 2024.

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 an open PhD position in my group. The project will develop advanced simulation algorithms to characterise strongly correlated system dynamics in both condensed matter and agent-based epidemic modelling.

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