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

# Papers

Zero-sum squares in $$\{-1,1\}$$-matrices with low discrepancy
Submitted
2020+
@article{johnston2020zero-sum, title={Zero-sum squares in {$\{-1,1\}$}-matrices with low discrepancy}, author={Johnston, Tom}, journal={arXiv preprint arXiv:2010.10310}, year={2020} }
Exact hyperplane covers for subsets of the hypercube
Submitted
2020+
@article{aaronson2020exact, title={Exact hyperplane covers for subsets of the hypercube}, author={Aaronson, James and Groenland, Carla and Grzesik, Andrzej and Johnston, Tom and Kielak, Bart{\l}omiej}, journal={arXiv preprint arXiv:2010.00315}, year={2020} }
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
Annales de l'Institut Henri Poincaré, Probabilités et Statistiques
2020 56(3) 2017–2027
@article{aru2020exceptional, 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={Annales de l'Institut Henri Poincar{\'e}, Probabilit{\'e}s et Statistiques}, volume={56}, number={3}, pages={2017--2027}, year={2020}, organization={Institut Henri Poincar{\'e}}, doi = {10.1214/19-AIHP1026} }

# 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.