Thesis research program

  • A new approach for the Fourier extension problem for the paraboloid. [arXiv]
  • We revisit the linear and multilinear theory for the Fourier Extension problem. Partial results so far include obtaining the full range of expected exponents for tensors in the linear setting, as well as the full range (up to endpoints in some cases) for all d-linear and k-linear variants when one of the functions involved in each problem is a tensor (this recovers Tao's bilinear theorem and Bennett-Carbery-Tao's d-linear estimate in this setting, for example). This is work in progress.


Notes

  • Notes on the Kakeya maximal conjecture and related problems. [PDF]
  • Notes on the bilinear restriction. [PDF]

Talks at colloquia and conferences

  • From needles and tubes to Fourier multipliers and beyond, Cornell University, 2017.
  • Lp regularity of avg. over curves and bounds for assoc. max. operators, Kopp, Germany, 2017.
  • Reconstructions from boundary measurements, Kopp, Germany, 2018.
  • Brascamp-Lieb inequalities, Cornell University, 2019.
  • On Bounds for Packings on a Sphere and in Space, Kopp, Germany, 2019.
  • The circle method, Cornell University, 2021.
  • The Fourier Extension problem through a time-frequency perspective, MSRI, 2021.

Invited seminar talks

  • Graduate students working group, MSRI, 2021.
  • Analysis seminar, ETH Zurich, 2021.
  • Analysis seminar, Universitat Bonn, 2021.
  • Analysis and PDE seminar, BCAM Bilbao, 2021.
  • Analysis seminar, Georgia Tech, 2021.
  • Analysis seminar, Virginia Tech, 2021.
  • Harmonic Analysis group seminar, MIT, 2021.
  • Analysis seminar, University of Wisconsin, 2021.
  • Harmonic analysis session, AMS Fall Western Sect. Meeting, 2021.
  • Analysis seminar, Universit\'e de Nantes, France, 2022.