Small cap decoupling for the moment curve in R^3

The partial differential equations and analysis seminar is the research seminar associated with the applied and nonlinear analysis, and the analysis and geometry programs.

schedule Date & time
17 May 2022 | 10:30 - 11:30am
person Speaker


Dominique Maldague (MIT)
next_week Event series


contact_support Contact
Contact name
Po-Lam Yung
Contact email

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Abstract: I will present the full solution to a small cap decoupling problem for the moment curve in R^3 motivated by a question about exponential sums. In particular, we prove Conjecture 2.5 in dimension 3 from the original small cap decoupling paper of Demeter, Guth, and Wang. Decoupling for the moment curve involves the following set-up. Begin with a function $f$ with Fourier transform supported on a small neighborhood of a curve. Break the curve up into pieces which are approximately linear blocks. Then we estimate the size of $f$ in terms of an expression with the Fourier projections onto each of these blocks. This is possible since the Fourier projections of $f$ onto different blocks cannot both be large for a long time, which we exploit using a high-low frequency argument. This is based on in-progress work in collaboration with Larry Guth.

The Zoom link for this talk is available here. If you are not currently affiliated with the ANU, please contact Po-Lam Yung for access.



Upcoming events in this series

28 Apr 2023 | 11am - 12pm