Thomas Karam

Since October 2025 I am a tenure-track Associate Professor at the School of Mathematical Sciences of Shanghai Jiao Tong University.
To write to me you can use thomas nospace karam at sjtu dot edu dot cn.

My top research priority is the development of the fundamental theory of the ranks of tensors.
Furthermore, I am highly interested in all kinds of questions in combinatorics, as well as geometric inequalities and information theory.

During the second semester of 2025-2026 I am teaching Modern Combinatorics, and taught Advanced Algebra during the first semester.

Earlier, I was a postdoctoral researcher at the University of Oxford (2022-2025), a doctoral student at the University of Cambridge (2018-2022), and an undergraduate up to Masters level at the ENS in Paris (2014-2018).

Below are my research manuscripts (links to arxiv versions, ordered by date of submission of the first version to arxiv, on the left):

• 15: Upcoming (with Peter Keevash) Extremal expansions by cubes in the torus.
  
  

• 14: 11/24 (with Peter Keevash) The structure of sets with cube-avoiding sumsets (12 p)
  Mathematika, 71 (4) (2025), e70041.
  
  

• 13: 08/24 Unions of intervals in codes based on powers of sets (13 p).
  European Journal of Combinatorics, 134 (2026), 104350.
  
  

• 12: 08/24 Three applications of coverings to difference patterns (25 p).
  SIAM Journal on Discrete Mathematics, 40 (1) (2026), 170-191.
  
  

• 11: 06/24 On entropy Marton-type inequalities and small symmetric differences with cosets of abelian groups (10 p).
  Submitted.
  
  

• 10: 05/24 On small densities defined without pseudorandomness (17 p).
  Finite Fields and Their Applications, 110 (2026), 102735.
  
  

• 9: 11/23 Simple proofs for lattice coverings and sparse tensors (15 p).
  European Journal of Combinatorics, 129 (2025), 103975. [EUROCOMB'23 special issue]
  
  

• 8: 10/23 The interplay between bounded ranks of tensors arising from partitions (25 p).
  Mathematika, 70 (4) (2024), e12277.
  
  

• 7: 09/23 On the expressive power of mod-p linear forms on the Boolean cube (26 p).
  Submitted.
  
  

• 6: 08/23 Small sunflowers and the structure of slice rank decompositions (45 p).
  Journal of the London Mathematical Society, 113 (3) (2026), e70485.
  Also (shorter version) in the conference proceedings of Innovations in Theoretical Computer Science (ITCS) 2024.
  
  

• 5: 06/23 (with Timothy Gowers) Low-complexity approximations for sets defined by generalizations of affine conditions (26 p). Submitted.
  
  

• 4: 05/23 Ranges of polynomials control degree ranks of Green and Tao over finite prime fields (25 p).
  Proceedings of the Edinburgh Mathematical Society. Published online doi:10.1017/S0013091526101382 (2026), 1-28.
  
  

• 3: 03/23 (with Jan Draisma) On subtensors of high partition rank (10 p).
  Proceedings of the American Mathematical Society, 152, (2024), 5083-5093.
  
  

• 2: 09/22 (with Timothy Gowers) Equidistribution of high-rank polynomials with variables restricted to subsets of F_p (42 p).
  In revision at Forum of Mathematics, Sigma.
  
  

• 1: 07/22 High-rank subtensors of high-rank tensors (69 p).
  In revision at Advances in Combinatorics.