Work with me

I am presently a Hooke Research Fellow in the Wolfson Centre for Mathematical Biology at the Mathematical Institute at Oxford, and will be moving to the University of Melbourne at the very start of 2025. As part of my move, I am looking for students who may be interested in pursuing a PhD in mathematical biology. I can offer projects in the following areas/themes:

Heterogeneity in biology.

Why do biological systems exhibit significant variability? Projects in this area will include the development of stochastic and spatial models of bacteria growth and adaptation. Interested students may also co-develop corresponding experimental models to expose bacteria to stochastic environments using computer-controlled bioreactors.

Identifiability of partial and stochastic differential equations.

Mathematical models are widely applied throughout biology and ecology to explain and consolidate complex systems. Many of the models that are routinely employed may, however, be unsuitable given the quantity and quality of experimental data that can be obtained in the lab. Projects in this area will involve the development of new and widely applicable theory that can be used to diagnose so-called parameter identifiability in mathematical biology.

Robust adaptive therapy in mathematical oncology.

Mathematical and statistical models have been shown, in recent years, to be an effective tool in the prediction and personalisation of cancer treatment. One way in which models have been effective is to develop treatment schedules that avoid or prolong the formation of drug resistant cancer subpopulations. The current state-of-the-art relies on deterministic models, very often with fixed or known patient-level parameters. Projects in this area will develop new mathematical and statistical models that realistically and robustly capture stochasticity in cancer progression, and the high-levels of individual-level uncertainty in the response of individual patients.

Full course details and application details can be found at https://research.unimelb.edu.au/study/how-to-apply. We would apply together by the Sept/Oct deadline in order for a successful student to start in February/March 2025. This timeline may be flexible.

Interested students should reach out to alex@alexbrowning.me.