Algorithmic regularity for polynomials and applications

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In analogy with the regularity lemma of Szemerédi [Sze75], regularity lemmas for polynomials proved by Green and Tao [GT09] and by Kaufman and Lovett [KL08] show that one can modify a given collection of polynomials F = {P1, . . ., Pm} into a new collection F' so that the polynomials in F' are \"pseudorandom\". These lemmas have various a...More