Biography
After studying for my undergraduate degree at the University of Bristol, I joined the University of Oxford to study my DPhil in Mathematics in 2021 under the supervision of Professor Ruth Baker (hyperlink: https://www.st-hughs.ox.ac.uk/people/professor-ruth-baker/) and Professor Philip Maini (hyperlink: https://people.maths.ox.ac.uk/maini/). I joined St Hugh’s in 2022 as a stipendiary lecturer, initially teaching Mathematical Modelling in Biology, but nowadays I teach a whole array of applied mathematics modules.
Research Interests
My research combines mathematics, biology, and data science methods to develop mechanistic and data-driven models of complex systems, with applications from microscopic cell migration to international public health interventions. I construct and apply a range of novel mathematical and computational approaches to investigate complex biological systems, focusing on the cell and tissue level for my PhD. These tools and modelling frameworks are often used in tandem with data provided from clinicians and experimental collaborators to gain real-world insight into unknown biological mechanisms. As such, I regularly enjoy collaborating across disciplines and internationally and, in general, I am interested in using a variety of tools from across mathematics to answer important questions for society, including those in medicine and healthcare.
Publications
Baker, R.E., Crossley, R.M., Falco, C. and Martina-Perez, S.F., 2025. Modelling collective cell migration in a data-rich age: challenges and opportunities for data-driven modelling. To appear in Cold Spring Harbour Press. arXiv 2504.19974.
Crossley, R.M., Maini, P.K., 2025. Ten simple rules for supervising an undergraduate or master’s research project. EdArXiv preprint.
Crossley, R.M., Maini, P.K. and Baker, R.E., 2025. Modelling the impact of phenotypic heterogeneity on cell migration: A continuum framework derived from individual-based principles. Bulletin of Mathematical Biology, 87(9), p123.
Martina-Perez, S.M., Johnson, S.W.S, Crossley, R.M., Kasemeier, J.C., Kulesa, P.M. and Baker, R.E., 2025. Optimal control in combination therapy for heterogeneous cell populations with drug synergies. To appear in Bulletin of Mathematical Biology. arXiv, 2502.12079.
Crossley, R.M. and Martina-Perez, S.F., 2024. Electrotaxis disrupts patterns of cell-cell interactions of human corneal epithelial cells in vitro. Biophysical Journal, 124(8), pp.1245-1254.
Browning, A.P., Crossley, R.M., Villa, C., Maini, P.K., Jenner, A.L., Cassidy, T. and Hamis, S., 2024. Identifiability of heterogeneous phenotype adaptation from low-cell-count experiments and a stochastic model. PLoS Computational Biology, 21(6), e1013202.
Crossley, R.M., Pietschmann, J.F. and Schmidtchen, M., 2025. Existence of weak solutions for a volume-filling model of cell invasion into extracellular matrix. Journal of Differential Equations, 428, pp.721-746.
Falcó, C., Crossley, R.M. and Baker, R.E., 2024. Travelling waves in a minimal go-or-grow model of cell invasion. Applied Mathematics Letters. 2024
Crossley, R.M., Painter, K.J., Lorenzi, T., Maini, P.K. and Baker, R.E., 2024. Phenotypic switching mechanisms determine the structure of cell migration into extracellular matrix under the ‘go-or-grow’ hypothesis. Mathematical Biosciences, p.109240.
Crossley, R.M., Johnson, S., Tsingos, E., Bell, Z., Berardi, M., Botticelli, M., Braat, Q.J., Metzcar, J., Ruscone, M., Yin, Y. and Shuttleworth, R., 2024. Modeling the extracellular matrix in cell migration and morphogenesis: a guide for the curious biologist. Frontiers in cell and developmental biology, 12, p.1354132.
Crossley, R.M., Maini, P.K., Lorenzi, T. and Baker, R.E., 2023. Traveling waves in a coarse‐grained model of volume‐filling cell invasion: Simulations and comparisons. Studies in Applied Mathematics, 151(4), pp.1471-1497.
Crossley, R., Agaoglou, M., Katsanikas, M. and Wiggins, S., 2021. From Poincaré maps to Lagrangian descriptors: The case of the valley ridge inflection point potential. Regular and Chaotic Dynamics, 26, pp.147-164.
