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Arthur King

I am currently a PhD student at the Centre for Doctoral Training in Mathematics for Real-World Systems at the University of Warwick, under the supervision of Professor Matthew Turner.

Research Interests

Swarming, collective motion, self-organization, cellular migration.

The collective motion of living entities – swarming - is one of the most striking aspects of biological life. This phenomenon is observed across many length scales, from herds of mammals and colonies of insects, to aggregations of cells and groups of sub-cellular motors. Mathematical modelling has become an essential tool, central to the study of such disparate systems.

My research can be categorised into two components. The first component is theoretical; I develop minimal models of collective motion and investigate their properties.

The second component is in more of an applied setting; I explore collective cell migration during vertebrae development. Cells coordinate their motion via complex biomolecular signalling and mechanical interactions, which are essential for proper development. I develop a novel biophysical model of cellular migration during Zebrafish embryo development. I then fit the model to data collected with fluorescence imaging techniques, to assess the importance of traction forces in driving the collective migration.

Industry Internship

  • I worked a 6-month placement at Legion Ltd, a former software company specialising in pedestrian dynamics. The role involved developing (c++ and python) novel tools to analyse data from pedestrian crowds, in order to support the calibration of an industry standard pedestrian simulator. London, 2017.

Academic Activities


  • King AEBT, Turner MS. 2021 Non-local interactions in collective motion. R. Soc. Open Sci. 8: 201536.


  • Teaching assistant for Modern Topics in Mathematical Modelling (MA999) for masters students on MSC in Mathematics for Real-World Systems, Mathematics Department, 2016/17, 2017/2018.
  • Seminar tutor for Quantitative Analysis for Management 1 (IB121) for first year undergraduates on BSc in Management/International Management, Warwick Business School, 2018/19.


  • Theory of Condensed Matter Group Scientific Meeting, University of Warwick, June 2019 (poster presented).
  • CECAM Workshop. Emerging Behaviour In Active Matter: Computational Challenges. University of Lincoln, June 2019 (talk presented).


  • 2014-2015 MSc Mathematics of Real-World Systems, University of Warwick
    Research Project: Investigating the Emergence of Collective Motion
    Group Project: Assessing the Impact of the Total Loss Absorbing Capacity (TLAC) proposal on Systemic Risk
  • 2008-2012 MSci Physics with Astrophysics, University of Bristol
    Research Project: Fractal Galaxy Clusters
    Awarded Winton Capital Management Prize for best project in Astrophysics



Centre for Complexity Science
Zeeman Building
University of Warwick