About
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
Reconstructing trees from small cards
Submitted
2021+
@article{groenland2021reconstructingtrees,
title={Reconstructing trees from small cards},
author={Groenland, Carla and Johnston, Tom and Scott, Alex and Tan, Jane},
journal={arXiv preprint arXiv:2103.13359},
year={2021}
}
Reconstructing the degree sequence of a sparse graph from a partial deck
Submitted
2021+
@article{groenland2021reconstructing,
title={Reconstructing the degree sequence of a sparse graph from a partial deck},
author={Groenland, Carla and Johnston, Tom and Kupavskii, Andrey and Meeks, Kitty and Scott, Alex and Tan, Jane},
journal={arXiv preprint arXiv:2102.08679},
year={2021}
}
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 \(\mathbb{F}_2^n\)
Journal of Combinatorial Theory, Series A
2021
181
105436
@article{aaronson2021cyclically,
title={Cyclically covering subspaces in {$\mathbb{F}_2^n$}},
author={Aaronson, James and Groenland, Carla and Johnston, Tom},
journal={Journal of Combinatorial Theory, Series A},
volume={181},
pages={105436},
year={2021},
}
Lipschitz bijections between boolean functions
Combinatorics, Probability and Computing
2020
1–13
@article{johnstonlipschitz,
title={Lipschitz bijections between boolean functions},
author={Johnston, Tom and Scott, Alex},
journal={Combinatorics, Probability and Computing},
pages={1--13},
publisher={Cambridge University Press}
}
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.