A copy of my current CV can be found here.
University of Oxford, Balliol College
Oxford, UK Graduated August 2022
D.Phil. in Mathematics
Doctoral thesis title: "Follow the leader: collective cell migration in cancer and developmental biology."
Supervisors: Prof. Philip K. Maini, Prof. Helen M. Byrne
Brown University
Providence, RI, USA Graduated May 2018
Honors Sc.B. in Applied Mathematics-Biology
Magna cum laude (highest honors awarded), Phi Beta Kappa, GPA: 4.0/4
Senior honors thesis title: "Long-time integration of reaction transport and application to coagulation kinetics."
Supervisors: Prof. Martin R. Maxey, Dr. Alireza Yazdani.
Apply statistics such as pair correlation functions to quantify spatial organisation within the microenvironment of tumours and link these descriptions with mechanistic mathematical models. Collaborate with experimental biologists to analyse images of mouse and human lung cancer biopsies. Construct mechanistic mathematical models of tumour-immune interactions to evaluate the extent to which spatial statistics can capture causative information. Train machine learning models on these quantitative descriptions to better predict patient outcomes from available data.
Granted a one-year postdoctoral fellowship funded by the Isaac Newton Institute (INI) and the Simons Foundation to attend the programme “Mathematics of Movement” and build an international collaborative network. Conduct independent research in the mathematical modelling of collective movement. Unite techniques from data science, statistics, and mathematical biology to create novel data-driven models to assess the impact of individual heterogeneity on collective behaviour.
Analysed mathematical frameworks called aggregation-diffusion equations to model long-range cellular interactions in collective migration and pattern formation. Applied Bayesian parameter estimation methods to fit these models to experimental and synthetic data. Collaborated with experimental biologists in Spain and the United States to explain their observations with mathematical modelling. Developed and programmed novel numerical algorithms for simulating models that mix elements of individual-based and continuous frameworks. Co-organised the July 2023 OxPDE workshop on Topics in Collective Migration, Neuroscience, and Parameter Estimation.
Investigated mathematical models for collective cell migration within the contexts of embryonic development and tumour-induced angiogenesis (blood vessel formation). Applied techniques from asymptotic analysis to demonstrate equivalences between several microscopic individual-based models (IBMs) and macroscopic population-level models for angiogenesis. Collaborated with theoreticians and experimentalists to create a new IBM for neural crest stem cell migration within a dynamic microenvironment. Identified dominant mechanisms directing cells and guided in vivo experimental design.
Developed and simulated a mathematical model for blood clotting (thrombosis) in a two-dimensional vessel experiencing blood flow. This project aimed to help physicians better analyse the development of blood clots over long time periods by making simulations of their onset more efficient and accurate.
Conducted genetic and biochemical screens for blood clotting (thrombosis) under the supervision of Dr. Jordan Shavit, a hematologist/oncologist, in a zebrafish animal model. Assisted in the development of new methods for identifying genetic and biochemical modifiers of thrombosis.
Kim J., Jeong H., Falco C., Hruska A.M., Martinson W.D., Marzoratti A., Araiza M. Yang H., Franck C., Carrillo J.A., Guo M., Wong I.Y. (preprint). "Collective transitions from orbiting to matrix invasion in 3D multicellular spheroids." bioRxiv bioRxiv:2025.02.10.636936. DOI: 10.1101/2025.02.10.636936
Martinson W.D., Volkening A., Schmidtchen M., Venkataraman C., Carrillo J. (2024). "Linking continuous and discrete models of cell birth and migration." Roy Soc Open Sci 11, 232002. arXiv:2308.16093. DOI: 10.1098/rsos.232002
Terragni F., Martinson W.D., Carretero M., Maini P.K., Bonilla L.L. (2023). "Soliton approximation in continuum models of leader-follower behavior." Physical Review E 108 (5), 054407. DOI: 10.1103/PhysRevE.108.054407
Martinson W.D., McLennan R., Teddy J.M., McKinney M.C., Davidson L.A., Baker R.E., Byrne H.M, Kulesa P.M., Maini P.K. (2023). "Dynamic fibronectin remodeling prevents collective cell jamming in a cell-based mathematical model." eLife 12, e83792. arXiv:2209.07794. DOI: 10.7554/eLife.83792
Martinson W.D., Ninomiya H., Byrne H.M., Maini P.K. (2021). "Comparative analysis of continuum angiogenesis models." Journal of Mathematical Biology 82 (21), online. DOI: 10.1007/s00285-021-01570-w
Martinson W.D., Byrne H.M., Maini P.K. (2020). "Evaluating snail-trail frameworks for leader-follower behavior with agent-based modeling." Physical Review E 102 (6), 062417. DOI: 10.1103/PhysRevE.102.062417
Martinson W.D., Byrne H.M., Maini P.K. (2019). "Multiscale modeling and simulation of traveling waves in biology: A review." Rendiconti di Matematica e delle sue Applicazioni 40 (7), 191-216.
Shea, K.G., Martinson W.D., Cannamela P.C., Richmond C.G., Fabricant P.D., Anderson A.F., Polousky J.D., Ganley T. J. (2018). "Variation in the medial patellofemoral ligament origin in the skeletally immature knee: An anatomic study." The American journal of sports medicine 46 (2), 363-369. DOI: 10.1177/0363546517738002
Richmond C.G., Green D.W., Cannamela P.C., Martinson W.D., Shea K.G. (2018). The distance between the hamstring grafts and the physis and apophysis of the proximal tibia – implications for pediatric ACL reconstruction and physeal arrest. Journal of ISAKOS: Joint Disorders & Orthopaedic Sports Medicine, 3 (6), 318-322. DOI: 10.1136/jisakos-2018-000222
Martinson W.D. (November 2022). "From sandcastles to economics and artificial intelligence: optimal transport through the years". The Oxford Scientist, Michaelmas Term 2022 volume, pp. 28-29. https://oxsci.org/optimal-transport-theory/
Martinson W.D. (March 2022). "Mathematical modelling for regenerative medicine: dream or reality?". The Oxford Scientist, Hilary Term 2022 volume, pp. 26-27. https://oxsci.org/mathematical-modelling-for-regenerative-medicine/
Invited short talk at Advances in Quantitative Neurobiology Workshop, University of Oxford, UK
Invited seminar talk at University of Nottingham Mathematical Medicine and Biology Seminar, online (University of Nottingham, UK)
Invited seminar talk at University College London Mathematical Biology Meeting, University College London, UK
Poster at 2024 London Mathematical Biology Annual Meeting, London, UK
Mini-symposium talk at 2024 European Conference for Theoretical and Mathematical Biology (ECMTB), Toledo, Spain
Mini-symposium talk at 2024 British Applied Mathematics Colloquium, University of Newcastle, UK
Invited seminar talk at University of Edinburgh Mathematical Biology Group Seminar, University of Edinburgh, UK
Invited mini-symposium talk at 2023 European Conference on Numerical Mathematics and Advanced Applications (ENUMATH), Lisbon, Portugal
Contributed talk at Isaac Newton Institute Workshop on Collective Behaviour, Isaac Newton Institute, Cambridge, UK
Contributed talk at Isaac Newton Institute Summer School on Mathematics of Movement, Isaac Newton Institute, Cambridge, UK
Invited workshop talk at 2023 Mathematical Biology: Applications and Analysis Workshop, TU Dresden, Germany
Invited seminar talk at TU Dresden Mathematical Biology Group Seminar, TU Dresden, Germany
Contributed talk at 2023 British Applied Mathematics Colloquium, University of Bristol, UK
Invited talk and poster at 2023 Gordon Research Conference on Neural Crest Cells and Placodes , Barga, Italy
Invited talk at 2023 Joint Mathematics Meetings, Boston, MA, USA
Invited mini-symposium talk at 2022 European Conference for Mathematical and Theoretical Biology, University of Heidelberg, Germany
Poster at Mathematical Models for Biomedical Sciences Summer School, Lake Como School of Advanced Studies, Como, Italy
Poster at Inference for Expensive Systems in Mathematical Biology Conference, Mathematical Institute, University of Oxford, UK
Contributed talk at 2022 British Applied Mathematics Colloquium, Loughborough University, UK
Contributed talk at 2021 Society for Mathematical Biology Annual Meeting, online
Talk at internal online symposium at Micro-to-Macro Modelling in Developmental Biology, University of Oxford Mathematical Institute, UK
Poster at 2020 Society for Mathematical Biology Annual Meeting, online
Poster at 2019 IMO Workshop, Moffitt Cancer Center, Tampa, FL, USA
Poster at Philip Maini's 60th Birthday Workshop, Mathematical Institute, University of Oxford, UK
Poster at 2019 Society for Mathematical Biology Annual Meeting, University of Montreal, Canada
Talk at University of Michigan Cardiovascular Center, Ann Arbor, MI, USA
Awarded a 1-year research fellowship by the Isaac Newton Institute (Cambridge, UK) and the Simons Foundation to attend the Mathematics of Movement programme and begin independent research in collaboration with UK-based faculty.
Accredited by the Higher Education Academy of the U.K. as meeting professional standards for the teaching of undergraduate students. Learned and applied evidence-based approaches to improve my teaching practices and lesson plans for first-year mathematics students.
Awarded at the 2021 Society for Mathematical Biology Annual Meeting in recognition of outstanding research presentation.
Awarded a 1.5-year full scholarship with stipend by the University of Oxford Mathematical Institute (equivalent to £34,000 GBP/year) to conclude my studies at the university, in recognition of my achievements as a scholar within the department.
Awarded a 2-year full scholarship with stipend by the Keasbey Memorial Foundation (equivalent to £34,000 GBP/year) to pursue graduate study at the University of Oxford, in recognition of my past achievements as a scholar and of my future leadership potential.
Awarded a three-month fully paid opportunity to conduct research with faculty members at the University of Michigan Cardiovascular Center (FCVC), in recognition of my interest and potential career in biomedical research.
Elected to the Rhode Island Alpha Chapter of Phi Beta Kappa in March 2017 during my junior year by my peers in recognition of outstanding academic achievement in studies spanning the liberal arts and sciences.
Elected to the Brown University chapter of the Sigma Xi scientific research honor society in recognition of sustained commitment to and excellence in scientific research during my undergraduate years.
Co-organiser of an early career researcher panel at the Isaac Newton Institute workshop “Measures and Representations of Interactions”. Moderated a four-member panel of senior mathematicians and research scientists by asking them about current challenges for early career researchers in science and mathematics.
Co-organizer of July 2023 workshop on Topics in Collective Migration, Neuroscience, and Parameter Estimation held in the University of Oxford Mathematical Institute. Invited conference speakers, arranged guest accommodation and meals, and led activities for attendees during the workshop.
Worked with the administration of the Mathematical Institute to review safety guidelines, such as fire safety protocols, within the department. Communicated issues raised by graduate students and postdoctoral researchers regarding safety and health.
Communicated with the administration of the Mathematical Institute to address issues affecting graduate students, such as funding or teaching. Designed and published a poster series at the Oxford University Mathematical Institute to highlight the historical contributions of women and non-binary mathematicians.
Member of the governing body for graduate students in Balliol College. Redesigned the Middle Common Room (MCR) website to improve accessibility for students. Managed the MCR website and mailing lists for graduate students.