## Proof of the $l^2$ decoupling conjecture

#### Ciprian DemeterIndiana University

We prove the $l^2$ Decoupling Conjecture for hypersurfaces with nonvanishing Gaussian curvature in the expected range of $L^p$ spaces. This has a wide range of important consequences. One of them is the validity of the Discrete Restriction Conjecture, which in turn implies the full range of expected $L^p_{x,t}$ Strichartz estimates for both classical and irrational tori. Another one is an improvement in the range for the discrete restriction theory for lattice points on the sphere. Various connections with Incidence Geometry and Number Theory are also discussed. This is joint work with Jean Bourgain.

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