Projects & Students

Prospective PhD Students

I am open to inquiries from enthusiastic, prospective PhD students on all topics close to my research interests. Currently, I am most interested in students related to projects in microbial ecology (dynamical systems/applied PDE), forest-savanna models (mean-field theory/applied PDE), and mathematical epidemiology (within-host malaria models/applied PDE).

Please contact me directly to discuss potential projects and funding sources at Durham (such as the DDTF, CSC or other schemes).

Undergraduate Summer Research

I have been fortunate to supervise many excellent undergraduate researchers at Brandeis, Princeton, and Durham universities, and I personally benefited enormously from undertaking summer research as an undergrad. I am always open to discussing potential summer research opportunities with interested students.

Recently, I have had students funded by summer research bursaries from the London Mathematical Society and Durham’s Biophysical Sciences Institute; applications for these schemes are due around January, so please contact me as early as possible to discuss funding opportunities. Durham Maths students might also consider joining our structured Mathematics Summer Research Award scheme [Durham login required].

A selection of recent students and projects I have supervised are listed below.

Summer 2025

  • Matthew Black (Durham, year 3) – Backward bifurcations in malaria models [supported by the London Mathematical Society. Next position – PhD student, Cambridge University].
  • Francesca Darkins (Durham, year 1) – Ecosystem Resilience in a Changing Climate [supported by a NERC Research Experience Placement bursary]
  • Aidan Flatt (Durham, year 2) – The mathematics of pattern formation [supported by a Collingwood College summer bursary].
  • Thomas Mills (Durham, year 3) – Mathematical modelling of vegetation dynamics.
  • Sarah Mitchell (Durham, year 2) – Modelling resilience in medicine and ecology [supported by a Collingwood College summer bursary].

Summer 2024

  • Thomas Shaw (Durham, year 3) – Microbial coexistence with resource toxicity [supported by the Durham Biophysical Sciences Institute. Next position – PhD student, University of Oxford].
  • Ewan Green (Durham, year 3) – Mathematical modelling of microbial coexistence [supported by the London Mathematical Society].

Undergraduate research at Princeton and Brandeis

  • Kimberly Shen (Princeton, Summer 2023 & Senior Thesis) – Fire spread in forest-savanna ecosystems [Princeton PACM Certificate Best Research Project Prize – paper in the Journal of Mathematical Biology].
  • Oliver Liang (Brandeis, Fall 2021) – Collective dynamics of mobile particles.
  • Jingman Li and Yuning Liu (Brandeis, Fall 2020) – Network epidemic models.
  • Hange Zhu (Brandeis, Spring 2020) – Pattern formation in heterogeneous domains.
  • Hanyu Song (Brandeis, Summer 2019) – Mathematical models of somitogenesis.

Durham Final Year Projects

Below is a list of my past/current Durham Final Year undergraduate project proposals (all final year Durham Mathematics students complete a thesis that counts as a double module):