Thomas Karam

Since September 2025 I am tenure-track faculty at Shanghai Jiao Tong University. To write to me you can use thomas nospace karam at sjtu dot edu dot cn.

My main research interests are tensors, combinatorics, geometric inequalities, and information theory.

I am currently teaching Advanced Algebra in the first semester of 2025-2026.

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).

Manuscripts (arxiv versions, from most to least recent date of submission of the first version to arxiv, indicated 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). Published in Mathematika.
  
  

• 13: 08/24 Unions of intervals in codes based on powers of sets (13 p). Submitted.
  
  

• 12: 08/24 Three applications of coverings to difference patterns (25 p). Accepted to SIAM Journal of Discrete Mathematics.
  
  

• 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). Published in Finite Fields and their Applications.
  
  

• 9: 11/23 Simple proofs for lattice coverings and sparse tensors (15 p). Published in the European Journal of Combinatorics (special issue).
  
  

• 8: 10/23 The interplay between bounded ranks of tensors arising from partitions (25 p). Published in Mathematika.
  
  

• 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). ITCS 2024. In revision at the Journal of the London Mathematical Society.
  
  

• 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). In revision at Proceedings of the Edinburgh Mathematical Society.
  
  

• 3: 03/23 (with Jan Draisma) On subtensors of high partition rank (10 p). Published in Proceedings of the American Mathematical Society.
  
  

• 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.