Ingredients of the proof of decoupling
Introductory Workshop: Harmonic Analysis January 23, 2017 - January 27, 2017
Location: MSRI: Simons Auditorium
Analytic number theory
Fourier analysis
PDE
decoupling
harmonic analysis
42B20 - Singular and oscillatory integrals (Calderón-Zygmund, etc.)
52A35 - Helly-type theorems and geometric transversal theory
11N25 - Distribution of integers with specified multiplicative constraints
28-XX - Measure and integration {For analysis on manifolds, see 58-XX}
Ingredients Of The Proof Of Decoupling
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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Guth Notes
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Ingredients Of The Proof Of Decoupling
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06-Guth-2.mp4
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