On Trilinear Oscillatory Integrals: Three's a party - Colloqium

Friday, February 21, 2020 - 4:00pm
Strickland 105
Michael Christ, UC Berkeley

Abstract: Integrals with rapidly oscillating factors and their cousins, exponential sums, arise in many mathematical contexts. For instance, Plancherel's inequality for the Fourier transform, one of the most fundamental inequalities of all, can be viewed as a bilinear oscillatory integral inequality.

The theory of upper bounds for multilinear oscillatory integral forms of degree three and higher is far less developed. Some inequalities for the trilinear case will be presented, and the  relatively elementary) leading ideas underlying them will be exposed in broad terms.   A dichotomy between structure and pseudorandomness is a key theme. Additive combinatorics  Szemeredi's theorem), the theory of weak limits of solutions of nonlinear partial differential equations, web geometry, and multiscale analysis will make appearances in the story.

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