All reports by Author Hamed Hatami:

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TR14-040
| 30th March 2014
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Hamed Hatami, Pooya Hatami, Shachar Lovett#### General systems of linear forms: equidistribution and true complexity

Revisions: 1

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TR13-087
| 4th June 2013
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Hamed Hatami, Shachar Lovett#### Estimating the distance from testable affine-invariant properties

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TR12-184
| 26th December 2012
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Arnab Bhattacharyya, Eldar Fischer, Hamed Hatami, Pooya Hatami, Shachar Lovett#### Every locally characterized affine-invariant property is testable.

Revisions: 1

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TR11-029
| 6th March 2011
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Hamed Hatami, Shachar Lovett#### Correlation testing for affine invariant properties on $\mathbb{F}_p^n$ in the high error regime

Revisions: 1

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TR10-181
| 21st November 2010
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Hamed Hatami, Shachar Lovett#### Higher-order Fourier analysis of $\mathbb{F}_p^n$ and the complexity of systems of linear forms

Hamed Hatami, Pooya Hatami, Shachar Lovett

The densities of small linear structures (such as arithmetic progressions) in subsets of Abelian groups can be expressed as certain analytic averages involving linear forms. Higher-order Fourier analysis examines such averages by approximating the indicator function of a subset by a function of bounded number of polynomials. Then, to approximate ... more >>>

Hamed Hatami, Shachar Lovett

Let $\cal{P}$ be an affine invariant property of functions $\mathbb{F}_p^n \to [R]$ for fixed $p$ and $R$. We show that if $\cal{P}$ is locally testable with a constant number of queries, then one can estimate the distance of a function $f$ from $\cal{P}$ with a constant number of queries. This ... more >>>

Arnab Bhattacharyya, Eldar Fischer, Hamed Hatami, Pooya Hatami, Shachar Lovett

Let $\mathbb{F} = \mathbb{F}_p$ for any fixed prime $p \geq 2$. An affine-invariant property is a property of functions on $\mathbb{F}^n$ that is closed under taking affine transformations of the domain. We prove that all affine-invariant property having local characterizations are testable. In fact, we show a proximity-oblivious test for ... more >>>

Hamed Hatami, Shachar Lovett

Recently there has been much interest in Gowers uniformity norms from the perspective of theoretical computer science. This is mainly due to the fact that these norms provide a method for testing whether the maximum correlation of a function $f:\mathbb{F}_p^n \rightarrow \mathbb{F}_p$ with polynomials of degree at most $d \le ... more >>>

Hamed Hatami, Shachar Lovett

In this article we are interested in the density of small linear structures (e.g. arithmetic progressions) in subsets $A$ of the group $\mathbb{F}_p^n$. It is possible to express these densities as certain analytic averages involving $1_A$, the indicator function of $A$. In the higher-order Fourier analytic approach, the function $1_A$ ... more >>>