Dr Thomas Karam
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Woodstock Road
Oxford
OX2 6GG
Thomas Karam, Simple proofs for lattice coverings and sparse tensors. https://arxiv.org/pdf/2311.03344.pdf. European Journal of Combinatorics (special issue) (2024).
Thomas Karam, The interplay between bounded ranks of tensors arising from partitions https://arxiv.org/abs/2310.11356. Mathematika (2024).
Thomas Karam, Small sunflowers and the structure of slice rank decompositions https://arxiv.org/abs/2308.07101 (2023). Innovations in Theoretical Computer Science (ITCS) 2024.
Jan Draisma and Thomas Karam, On subtensors of high partition rank. https://arxiv.org/pdf/2303.03485.pdf. Proceedings of the American Mathematical Society (2024).
Timothy Gowers and Thomas Karam, Equidistribution of high-rank polynomials with variables restricted to subsets of F_p https://arxiv.org/abs/2209.04932 (2022). In revision at Forum of Mathematics, Sigma.
Thomas Karam, High-rank subtensors of high-rank tensors https://arxiv.org/abs/2207.08030 (2022). In revision at Advances in Combinatorics.
Primary research interests:
- Basic properties of the ranks of tensors
- Polynomials in finite fields
- Ramsey theory
- Analysis of Boolean functions
- Geometric inequalities
- Extremal and stability inequalities
- Number theory
- Information theory