Preprints

Good bounds for sets lacking skew corners

A note on transverse sets and bilinear varieties

Approximate quadratic varieties

Bilinear Bogolyubov argument in abelian groups

An inverse theorem for Freiman multi-homomorphisms (with Tim Gowers)

A quantitative inverse theorem for the U⁴ norm over finite fields (with Tim Gowers)

Small Sets with Large Difference Sets

Published papers

Quantitative inverse theorem for Gowers uniformity norms U⁵ and U⁶ in F₂ⁿ to appear in Canadian Journal of Mathematics.

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.