OUPPS (Open University People Profile System)

Biography

Professional biography

I am a Lecturer of Applied Mathematics at the Open University. After receiving an MMath from Manchester University in 2012, I obtained my PhD from the University of Leicester in 2016 under the supervision of Alex Clark. I then undertook a 4 year position in Bielefeld Unviersity as a postdoctoral researcher as a member of the Aperiodic Order group of Michael Baake. I joined the Open University from there in May 2020.

I am the student research experience coordinator for the School of Mathematics & Statistics. For more information about these schemes and how to apply, see here or contact me directly by email.

Research interests

My research is focused on symbolic dynamics, as well as the topology, dynamics and spectral theory of aperiodic tilings and quasicrystals. Specific topics include:

The representation of tiling spaces as inverse limits of branched manifolds and their Čech cohomology
The dynamics of tilings and bi-infinite sequences - especially those arising from substitutions, S-adic systems and random substitutions, as well as cut and project sets
Applications of aperiodic order to other areas of mathematics - specifically the study of combinatorial game theory, dimension groups and Diophantine approximation

I also have interests in general topological dynamics and algebraic topology as a whole. I have a particular fondness for the applications of algebraic topology to knot theory and braids.

The above image is a Barge Diamond complex which was automatically generated by the program Grout.

Grout

Developed by myself and Scott Balchin, Grout is a free user-friendly program for Windows and Mac which can calculate various topological and combinatorial properties of symbolic substitutions.
For an explanation of the computations that Grout performs, we have provided documentation on the arXiv.
You can download Grout from Github.

Teaching interests

I am involved in the production and presentation of several undergraduate and postgraduate modules in Mathematics, including MST124 - Essential Mathematics 1, MST326 - Mathematical Methods and Fluid Mechanics, MST374 - Computational Applied Mathematics, M823 - Analytic Number Theory I and M840 - Dissertation in Mathematics (Topic: Aperiodic Tilings and Symbolic Dynamics).

Projects

Support of joint research group: The Grimm Network

Our goal is to sustain the existing network, bringing together all facets of the aperiodic order community in the UK.The network continues the pioneering work of our late colleague Prof. Uwe Grimm, who throughout his career wasinstrumental in facilitating the collaboration of UK researchers from diverse mathematics and physics backgrounds.Since 2019, Uwe spearheaded an ambitious program of monthly online meetings for the Aperiodic Ordercommunity. Building on this solid foundation, and following a successful first-of-its-kind workshop betweenmathematicians, physicists, engineers and artists at the Open University in June 2022, we have hosted at least twoin-person meetings per year since 2023, strengthening links in the community and fostering new ones and we aim to continue this program. The network has connected researchers across disciplines, including dynamical systems,discrete geometry, mathematical physics, materials science, operator algebras, combinatorics, and others. Inparticular, the network is hosted by nodes at the Open University (Dan Rust), Queen Mary University (ReemYassawi), University of Bristol (Felix Flicker), University of Derby (Petra Staynova), University of Exeter (Tony Samuel),University of Glasgow (Mike Whittaker), University of Leeds (Alastair Rucklidge), University of Liverpool (RonanMcGrath), University of Manchester (Yotam Smilansky), and Oxford University (Nick Jones). It is notable that all thedisciplines above are represented through research activity at the nodes, and each is eager to continue exploringresearch directions with the others. The principal funding for the network was secured for the first three years in2023 via an EPSRC New Investigator Award of Dr. Felix Flicker, one of the principal organisers of the Network, andwhich has recently been extended to 2027. We are seeking support from the LMS to bolster the scope of the eventsin 2026, and to potentially become a primary funding source of the network in subsequent years (if we are able torenew the network), necessarily with a reduced scope, unless additional funding is obtained from other sources.