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Thursday, October 9, 2014

**Abstract:** I will present some recent progress on the distribution of quadratic Weyl sums. For example, the exact asymptotic in the tail distribution is related to counting integer solutions on Vinogradov's quadric. This result also comes with an explicit power saving. Our method uses the modularity of the Jacobi theta function and equidistribution of long closed horocycles. Joint work with J. Marklof (Bristol)