This proposal consists of two intimately related programmes. The aim of Programme 1 is to make major contributions to the celebrated restriction theory for the Fourier transform and combinatorial problems of Kakeya-type using emerging multilinear techniques. The aim of Programme 2 is to develop a multilinear perspective on a much broader family of curvature-related problems in harmonic analysis, including important classes of Radon-like transforms that arise naturally in the theory of dispersive partial differential equations.
The specific objectives represent major challenges at the emerging frontiers of harmonic analysis with a variety of disciplines, including geometric analysis (encompassing heat-flow methods and convex geometry), affine geometry and algebraic topology.
Fields of science
Call for proposal
See other projects for this call