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Explore open questions related to decoupling in this 49-minute lecture by Larry Guth from MIT, presented at the Hausdorff Center for Mathematics. Delve into the concept of sharp examples for decoupling, examining various ways to precisely formulate this question. Investigate how the framing of the question affects the number and nature of known sharp examples, with some cases revealing rare examples based on number theoretic structure. Consider whether all nearly sharp examples necessarily possess number theoretic properties. Gain insights into the connections between this topic and problems in harmonic analysis, and understand the current limitations of harmonic analysis techniques in addressing these questions.
