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HA Postdoc Seminar: An Application of $\ell^2$ Decoupling February 24, 2017 (12:00 PM PST - 12:50 PM PST)
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Location: MSRI: Simons Auditorium
Speaker(s) Bobby Wilson (Massachusetts Institute of Technology)
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(Colloquium-Style Talk)

In this talk, we will discuss work concerning the improvement of Strichartz estimates for the cubic nonlinear Schr\"odinger equation on the irrational torus.  A surprisingly crucial aspect of the original problem, for the rational torus, is that we can reduce our estimates to counting lattice points contained in convex bodies.  However, there is a sharp contrast,  in which techniques are applicable, between the case of the irrational torus and the rational torus.  We will discuss how $\ell^2$-decoupling allows us to bridge the gap between the two cases.  (Joint with G. Staffilani, C. Fan, H. Wang)

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