I'm currently working towards a DPhil in combinatorics at the University of Oxford under the supervision of Alex Scott. Before starting my DPhil in 2017 I did an MMath in Oxford.

My main reserach interest is extremal combinatorics, and I tend to spend most of my time working on problems that involve hypercubes in some way.

# Papers

Cyclically covering subspaces in $$\mathbb{F}_2^n$$
Submitted
2019+
@article{aaronson2019cyclically, title={Cyclically covering subspaces in $\mathbb{F}_2^n$, author={Aaronson, James and Groenland, Carla and Johnston, Tom}, journal={arXiv preprint arXiv:1903.10613}, year={2019} }
Lipschitz bijections between boolean functions
Submitted
2018+
@article{johnston2018lipschitz, title={Lipschitz bijections between boolean functions}, author={Johnston, Tom and Scott, Alex}, journal={arXiv preprint arXiv:1812.09215}, year={2018} }
Intersection sizes of linear subspaces with the hypercube
Journal of Combinatorial Theory, Series A
2020 170 105-142
@article{groenland2020intersection, title={Intersection sizes of linear subspaces with the hypercube}, author={Groenland, Carla and Johnston, Tom}, journal={Journal of Combinatorial Theory, Series A}, volume={170}, pages={105-142}, year={2020}, publisher={Elsevier} }
Exceptional graphs for the random walk
Submitted
2019+
@article{aru2018exceptional, title={Exceptional graphs for the random walk}, author={Aru, Juhan and Groenland, Carla and Johnston, Tom and Narayanan, Bhargav and Roberts, Alex and Scott, Alex}, journal={arXiv preprint arXiv:1805.06277}, year={2018} }

# Contact

If you have any questions or comments about some interesting maths (or the maths I've done), feel free to send me an email at thomas.johnston@lmh.ox.ac.uk.