William Martinson

D.Phil. (University of Oxford), Sc.B. (Brown University)

Postdoctoral Research Associate

+44 1865 615192

Contact form

ORCID iD

https://orcid.org/0000-0002-3590-606X

Research groups

Address

Mathematical Institute
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Woodstock Road
Oxford
OX2 6GG

Recent publications

Dynamic fibronectin assembly and remodeling by leader neural crest cells prevents jamming in collective cell migration

Martinson, W McLennan, R Teddy, J McKinney, M Davidson, L Baker, R Byrne, H Kulesa, P Maini, P (16 Sep 2022)

Comparative analysis of continuum angiogenesis models

Martinson, W Byrne, H Ninomiya, H Maini, P Journal of Mathematical Biology volume 82 (23 Feb 2021)

Evaluating snail-trail frameworks for leader-follower behavior with agent-based modeling

Martinson, W Maini, P Byrne, H Physical Review E volume 102 (14 Dec 2020)

Multiscale modeling and simulation of traveling waves in biology: a review

Martinson, W Byrne, H Maini, P Rendiconti di Matematica e delle sue Applicazioni volume 40 issue 7 191-216 (29 Aug 2019)

Dynamic fibronectin assembly and remodeling by leader neural crest cells prevents jamming in collective cell migration.

Baker, R eLife

Further details

I am interested in the development and analysis of mathematical models for collective migration -- the coordinated movement of multiple individuals. This phenomenon is ubiquitous throughout biology: it plays a crucial role in successful embryonic development, for instance, as certain stem cells known as the neural crest travel throughout the embryo to help form the skeletal and nervous systems. A similar process also occurs during the formation of new blood vessels (where it is also known as angiogenesis). Even particular species of animals, such as starlings and barracuda, are known to form intricate flocking and swarming patterns when groups move together.

However, the particular means by which cells coordinate their movements are not well characterised in many biological contexts. Mathematical modelling can help supply new insight into how collective migration emerges from individual-level interactions, as it can tractably evaluate different biological hypotheses in an abstract setting, explore how certain mechanisms contribute to group behaviour, and guide the design of new experiments in collaboration with biologists. This is the goal of my research.

Prizes, awards, and scholarships

University of Oxford Mathematical Institute Graduate Scholarship - Awarded September 2020

Keasbey Memorial Foundation Graduate Scholarship - Awarded December 2017

Teaching

Teaching Experience:

College Tutor - Balliol College, Oxford
- Academic Year 2022-2023 - Numerical Analysis (A7)
- Academic Year 2022-2023 - Multivariable Calculus (M5)
Intercollegiate Tutor - Mathematical Institute, Oxford
- Academic Year 2022-2023 - Perturbation Methods (C5.5)
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)
- Academic Year 2020-2021 - Statistics and Data Analysis (M5)
- Academic Year 2021-2022 - Probability (M3)
- Academic Year 2021-2022 - Introductory Calculus (M3)
- Academic Year 2021-2022 - Multivariable Calculus (M5)
- Academic Year 2021-2022 - Statistics and Data Analysis (M3)

Last Updated January 2023