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This year's topic is "Additive combinatorics and applications." We will introduce various methods from additive combinatorics, establish the sum-product theorem over finite fields and derive various a
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We consider sums of oscillating functions on intervals in cyclic groups of size close to the square root of the size of the group. We first prove non-trivial estimates for intervals of length slightly larger than this square root (bridging the "Polya-Vinog ...