2 Instructor : Larry Guth Transcribed By
نویسنده
چکیده
Question 1.2. Suppose g(k) is the least number of powers to make Theorem 1.1 hold. How big is g(k)? To provide some intuition, take n = 2−1. In its decomposition any ai can’t be greater than 1, since 2 k > 2 − 1. Therefore, ai = 1 for all i and g(k) ≥ s = 2 − 1. The real value of g(k) is only a little worse than that. Thus, the number g(k) grows at least exponentially with respect to k. However, we have this estimate because some small n force it to be. Instead, one may ask what happens when n is large enough:
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Instructor: Larry Guth Transcribed by Jonathan Tidor
One hint that Theorem 0.1 might be more tractable than Theorem 0.2 is that the maximum value of p is the critical exponent in multilinear restriction. Our proof of Theorem 0.1 indeed uses multilinear restriction as an input. This lecture is divided into 3 parts. First are the “multiscale tools”; a statement of some of the properties of the decoupling problem that makes arguments at different sc...
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