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Title:
Ingredients of the proof of decoupling
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Abstract:
The ingredients of the proof In this lecture, we will learn the different tools that go into the proof of the decoupling theorem for the parabola. The ingredients are actually fairly simple: orthogonality, geometric estimates about how rectangles in different directions intersect each other, and induction on scales. It is remarkable how much leverage Bourgain and Demeter were able to get by looking at the problem at many scales. I will focus on this tool, and try to explain how looking at many scales helps us to get better estimates.
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