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. A selection of recent students and projects are listed below.

Summer 2025

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

Summer 2024

  • Thomas Shaw (Durham) – Microbial coexistence with resource toxicity [supported by the Durham Biophysical Sciences Institute. Next position – PhD student, University of Oxford].
  • Ewan Green (Durham) – 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].
  • 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):