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Lovett, Shachar

doi:10.4086/toc.gs.2015.006

Cited by 4 publications

(3 citation statements)

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“…In the case of quadratics d = 1, we have f U 2 = f 4 which gives δ = Ω( 2 ). The case of d = 2 is already nontrivial and the best known lower-bound for δ is quasi-polynomial in , which follows from a result of Sanders on the Bogolyubov-Ruzsa conjecture (Sanders [71], see also Lovett [58,59]).…”

Section: The Inverse Theorem For Gowers Normsmentioning

confidence: 97%

“…The other ingredient required is the structure of sets S for which S + S is not much larger than S. Here, the best result to date is by Sanders [71]. See also the survey by Sanders [72] for more details, and the exposition by Lovett [59] giving a simplified proof for G = F n 2 . Below, we present the result specialized to the case of G = F n 2 .…”

Section: Thus We Havementioning

confidence: 99%

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Higher-order Fourier Analysis and Applications

Hatami¹,

Hatami²,

Lovett³

2019

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Fourier analysis has been extremely useful in many areas of mathematics. In the last several decades, it has been used extensively in theoretical computer science. Higher-order Fourier analysis is an extension of the classical Fourier analysis, where one allows to generalize the "linear phases" to higher degree polynomials. It has emerged from the seminal proof of Gowers of Szemerédi's theorem with improved quantitative bounds, and has been developed since, chiefly by the number theory community. In parallel, it has found applications also in theoretical computer science, mostly in algebraic property testing, coding theory and complexity theory.The purpose of this book is to lay the foundations of higherorder Fourier analysis, aimed towards applications in theoretical computer science with a focus on algebraic property testing.

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Section: The Inverse Theorem For Gowers Normsmentioning

confidence: 97%

Section: Thus We Havementioning

confidence: 99%

Higher-order Fourier Analysis and Applications

Hatami¹,

Hatami²,

Lovett³

2019

Self Cite

View full text Add to dashboard Cite

show abstract

“…We state below his result for F n 2 ; his result applies to general Abelian groups as well (with the exponent 4 replaced by 6). Interested readers may also refer to an exposition [49] of the proof over F n 2 .…”

Section: Marton's "Polynomial Freiman-ruzsa Conjecture"mentioning

confidence: 99%