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Distribution of points in varieties: various aspects and their interaction

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Random sphere, disk, and annulus

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The C^3 problem: error-correcting codes with a constant rate, constant distance, and constant locality.

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The Fontaine-Mazur conjecture in dimension two

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Height Gaps, the Margulis Lemma and Almost Laws

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L-functions, functoriality, and quantization

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How round is a Jordan curve?

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Thresholds

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Projection theorems and applications

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Arithmetic algebraization and arithmetic groups

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