Quantitative inverse theorem for Gowers uniformity norms $\mathsf{U}^5$ and $\mathsf{U}^6$ in $\mathbb{F}_2^n$

Inverse problems of additive number theory, including sumsets (11P70) Group actions on combinatorial structures (05E18) Combinatorial aspects of groups and algebras (05E16)

Cites Work

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The inverse conjecture for the Gowers norm over finite fields in low characteristic
Linear forms and higher-degree uniformity for functions on $\mathbb F^n_p$
Linear equations in primes
On the Bogolyubov-Ruzsa lemma
Regularity and inverse theorems for uniformity norms on compact abelian groups and nilmanifolds
The partition rank of a tensor and $k$-right corners in $\mathbb{F}_q^n$
The structure theory of nilspaces. I
The structure theory of nilspaces. III: Inverse limit representations and topological dynamics
Polynomial bound for partition rank in terms of analytic rank
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The distribution of polynomials over finite fields, with applications to the Gowers norms
The structure theory of Nilspaces II: Representation as nilmanifolds
http://discreteanalysisjournal.com/article/2105-notes-on-nilspaces-algebraic-aspects
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A note on extensions of multilinear maps defined on multilinear varieties
Polynomial bound for the partition rank vs the analytic rank of tensors
AN INVERSE THEOREM FOR THE GOWERS $U^3(G)$ NORM
Approximately symmetric forms far from being exactly symmetric
An inverse theorem for the Gowers $U^{s+1}[N$-norm]
A new proof of Szemerédi's theorem
Inverse theorem for certain directional Gowers uniformity norms
Nilspace Factors for General Uniformity Seminorms, Cubic Exchangeability and Limits
Bias vs Structure of Polynomials in Large Fields, and Applications in Information Theory

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Quantitative inverse theorem for Gowers uniformity norms \(\mathsf{U}^5\) and \(\mathsf{U}^6\) in \(\mathbb{F}_2^n\)