Preprints
General inverse theory for the U4 norm
Möbius function is strongly orthogonal to polynomial phases over Fp[t] (with Žarko Ranđelović)
Quasipolynomial inverse theorem for the U4(Fpn) norm
Approximate quadratic varieties
An inverse theorem for Freiman multi-homomorphisms (with Tim Gowers)
Published papers
A note on transverse sets and bilinear varieties to appear in Mathematical Proceedings of the Cambridge Philosophical Society.
Good bounds for sets lacking skew corners Combinatorica 46 (2026), paper 2.
Low-codimensional Subvarieties Inside Dense Multilinear Varieties Proceedings of the 13th European Conference on Combinatorics, Graph Theory and Applications EUROCOMB '25 (2025), 904-909.
Bilinear Bogolyubov argument in abelian groups Discrete Analysis 2024:20, 41 pp.
Quantitative inverse theorem for Gowers uniformity norms U5 and U6 in F2n Canadian Journal of Mathematics 76 (2024), 1289-1338.
An inverse theorem for certain directional Gowers uniformity norms Publications de l'Institut Mathematique 113 (2023), 1-56.
Approximately Symmetric Forms Far From Being Exactly Symmetric Combinatorics, Probability and Computing 32 (2023), 299-315.
A note on extensions of multilinear maps defined on multilinear varieties (with Tim Gowers) Proceedings of the Edinburgh Mathematical Society 64 (2021), 148-173.
An improved upper bound for the grid Ramsey problem Journal of Graph Theory 94 (2020), 509-517.
Classification theorem for strong triangle blocking arrangements Publications de l'Institut Mathematique 107 (2020), 1-36.
A bilinear version of Bogolyubov's theorem (with Tim Gowers) Proceedings of the American Mathematical Society 148 (2020), 4695-4704.
Polynomial bound for partition rank in terms of analytic rank Geometric and Functional Analysis 29 (2019), no. 5, 1503-1530.
Covering complete graphs by monochromatically bounded sets Applicable Analysis and Discrete Mathematics 13 (2019), 85-110.
Decomposing the Complete r-Graph (with Imre Leader and Ta Sheng Tan) Journal of Combinatorial Theory, Series A 154 (2018), 21-31.
Sets in Almost General Position Combinatorics, Probability and Computing 26 (2017), no. 5, 720-745.
Commuting Contractive Families Fundamenta Mathematicae 231 (2015), no. 3, 225-272.
Contractive Families on Compact Spaces Mathematika 60 (2014), no. 2, 444-462.
Unpublised manuscripts
A quantitative inverse theorem for the U4 norm over finite fields (with Tim Gowers)