Dr Joel Mitchell MSci, MA, PhD

Dr Joel Mitchell

Institute of Cancer and Genomic Sciences
Research Fellow

Contact details

Centre for Computational Biology
Institute of Cancer and Genomic Sciences
University of Birmingham
B15 2TT

Joel Mitchell is a Research Fellow in the Institute of Cancer and Genomic Sciences with an interest in topology and how it may be used to gain novel insights into large datasets.


  • PhD in Pure Mathematics, University of Birmingham, 2021

  • MA in Philosophy, University of Birmingham, 2016

  • MSci (Hons) in Mathematics, University of Birmingham, 2015


Joel Mitchell studied Mathematics, with a specialisation in topology, at the University of Birmingham, receiving an MSci in 2015. Following this, he studied for an MA in Philosophy at the same institution, with a primary interest in free will and classical theism. Since 2016, Joel has been studying for a PhD in Pure Mathematics at the University of Birmingham.


Joel’s research involves identifying underlying structure in a series of large biomedical datasets. During his PhD, Joel worked in topological dynamics, with a focus on the pseudo-orbit tracing property, limit sets, and mathematical notions of chaos.


Recent publications


Mitchell, J 2022, 'When is the beginning the end? On full trajectories, limit sets and internal chain transitivity', Topology and its Applications, vol. 306, 107934. https://doi.org/10.1016/j.topol.2021.107934

Good, C, Leek, R & Mitchell, J 2020, 'Equicontinuity, transitivity and sensitivity: the Auslander-Yorke dichotomy revisited', Discrete and Continuous Dynamical Systems, vol. 40, no. 4, pp. 2441-2474. https://doi.org/10.3934/dcds.2020121

Good, C, Macias, S, Meddaugh, J, Mitchell, J & Thomas, J 2020, 'Expansivity and unique shadowing', Proceedings of the American Mathematical Society, vol. 149, no. 2, pp. 671-685. https://doi.org/10.1090/proc/15204

Good, C, Mitchell, J & Thomas, J 2020, 'On inverse shadowing', Dynamical Systems. https://doi.org/10.1080/14689367.2020.1739228

Good, C, Mitchell, J & Thomas, J 2020, 'Preservation of shadowing in discrete dynamical systems', Journal of Mathematical Analysis and Applications, vol. 485, no. 1, 123767, pp. 1-39. https://doi.org/10.1016/j.jmaa.2019.123767

Good, C, Mitchell, J & Meddaugh, J 2020, 'Shadowing, internal chain transitivity and α-limit sets', Journal of Mathematical Analysis and Applications, vol. 491, no. 1, 124291. https://doi.org/10.1016/j.jmaa.2020.124291

Mitchell, J 2019, 'Orbital shadowing, ω-limit sets and minimality', Topology and its Applications, vol. 268, 106903. https://doi.org/10.1016/j.topol.2019.106903

View all publications in research portal

Culture and collections

Schools, institutes and departments

Services and facilities