William Martinson
Address
Mathematical Institute
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Woodstock Road
Oxford
OX2 6GG
My research interests lie in the field of Mathematical Oncology; specifically, I study multiscale approaches to modeling and simulating the process of angiogenesis, which is the process by which new blood vessels are created from existing vasculature. My current work focuses on investigating the relationship betweeen stochastic, discrete models of angiogenesis that are formulated at the cellular level to continuous approaches that focus on larger-scale (e.g., tissue-level) behavior.
I am interested in the development and analysis of mathematical models for collective cell migration -- the coordinated movement of multiple cells. Collective cell migration constitutes an important biological phenomenon: it plays a crucial role in successful embryonic development, for instance, as stem cells (known as the neural crest) migrate from what becomes an organism's spinal cord throughout the embryo to complete the formation of the skeletal and nervous systems. Collective cell migration also occurs during a process known as angiogenesis (the formation of new blood vessels from pre-existing ones): in this case, cells lining the walls of existing blood vessels must travel relatively far distances to a target site (such as a wound). However, the particular means by which cells coordinate their movements are not well characterised in many biological contexts. The mathematical modelling that I do can help supply new knowledge and insight into how collective cell migration is realised by evaluating different biological hypotheses in an abstract setting, exploring how certain mechanisms contribute to group behaviour, and guiding the design of new experiments in collaboration with biologists.
University of Oxford Mathematical Institute Graduate Scholarship - Awarded September 2020
Keasbey Memorial Foundation Graduate Scholarship - Awarded December 2017
Teaching Experience:
- Graduate Teaching Assistant - Mathematical Institute, Oxford
- Academic Year 2018-2019 - Further Mathematical Biology (B5.5)
- Academic Year 2018-2019 - Numerical Solutions to Differential Equations I (B6.1)
- Academic Year 2019-2020 - Further Mathematical Biology (B5.5)
- Academic Year 2019-2020 - Nonlinear Systems (MMSC, B5.6)
- Academic Year 2020-2021 - Mathematical Modelling (MMSC)
- Graduate Teaching Assistant - Balliol College, Oxford
- Academic Year 2020-2021 - Probability (M3)
- Academic Year 2020-2021 - Introductory Calculus (M3)
- Academic Year 2020-2021 - Multivariable Calculus (M5)
Last Updated March 2021