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Friday, January 28, 2022

**Abstract:** Abstract: While dispersive PDE's is known for the harmonic analysis that it requires as an input, periodic dispersive PDEs goes a step beyond and often requires a bit of number theoretic input. In particular, most of the known proofs for periodic Strichartz estimates comes from divisor counting arguments. In this talk, I will discuss the L^8 Strichartz estimate (an open problem) and the proofs surrounding easier cases of this estimate. The proofs will be somewhat introductory, and are excellent tools for understanding basic techniques in estimating exponential sums.