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I'm a National Science Foundation postdoctoral fellow in mathematics at UCLA, sponsored by Terence Tao. I received a B.S. in mathematics in 2011 from Caltech and a Ph.D. in mathematics in 2016 from the University of Wisconsin - Madison under the supervision of Andreas Seeger. The title of my thesis was "Multiplier Theorems, Square Function Estimates, and Bochner Riesz Means Associated With Rough Domains." I spent the 2016-2017 academic year as a Visiting Assistant Professor at the University of British Columbia. Here's my CV. Together with Polona Durcik, I organized the Caltech-UCLA joint analysis seminar.

  • Classical harmonic analysis. This is a rather broad interest of mine, but I'm particularly interested in questions related to the local smoothing, Bochner-Riesz, and Fourier restriction problems, characterization theorems for radial and quasiradial multipliers, endpoint estimates for Calderon-Zygmund operators, discrete harmonic analysis, and sparse domination.
  • Additive combinatorics, in particular questions related to sum-product phenomena and Falconer's distance problem.
  • Recently, I've become interested in dispersive PDE and random matrix theory.

    Manuscripts in preparation:
  • A discrete Stein-Wainger theorem with a restricted supremum (with Ben Krause and Michael Lacey).
  • Submitted and/or published articles:
  • Additive energy of regular measures in one and higher dimensions, and the fractal uncertainty principle (with Terence Tao). arXiv
    Ars Inveniendi Analytica (2021), Paper No. 1, 38 pp.
  • Upper and lower bounds on the rate of decay of the Favard curve length for the four-corner Cantor set (with Blair Davey and Krystal Taylor). arXiv,
    Indiana U. Math. J., to appear.
  • Discrete Analogues in Harmonic Analysis: Directional Maximal Functions in Z2 (with Ben Krause). arXiv, To appear, IMRN.
  • Spherical means on the Heisenberg group: stability of a maximal function estimate (with Theresa Anderson, Malabika Pramanik, and Andreas Seeger). arXiv, To appear, Journal d'Analyse Mathematique.
  • Directional maximal function along the primes. (with Polona Durcik, Ben Krause, and José Madrid). arXiv
    Publ. Mat. 65 (2021), 841--858.
  • A discrete Carleson theorem along the primes with a restricted supremum. (with Kevin Henriot, Ben Krause, Izabella Łaba, and Malabika Pramanik). arXiv
    Math. Z. 289 (2018), no. 3-4, 1033--1057.
  • Sparse bounds for pseudodifferential operators (with David Beltran). arXiv
    J. Anal. Math. 140 (2020), no. 1, 89--116.
  • Sparse domination of Hilbert transforms along curves (with Yumeng Ou). arXiv
    Math. Res. Lett. 25 (2018), no. 2, 415--436.
  • Improved endpoint bounds for the lacunary spherical maximal operator (with Ben Krause). arXiv
  • Radial Fourier Multipliers in R3 and R4. arXiv
    Anal. PDE. 11 (2018), no. 2, 467--498.
  • A discrete Carleson theorem along the primes with a restricted supremum (with Kevin Henriot, Ben Krause, Izabella Łaba and Malabika Pramanik). arXiv
    Math. Z. 289 (2018), no. 3-4, 1033--1057.
  • On the square function associated with generalized Bochner-Riesz means arXiv
    Ind. Univ. Math. J. 66 (2017), no. 6, 2205--2238.
  • New Lp bounds for Bochner-Riesz multipliers associated with convex planar domains with rough boundary. arXiv
  • Multiplier transformations associated to convex domains in R2. arXiv
    J. Geom. Anal. 26 (2016), no. 4, 3129--3175.
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