lastnamefirstinitial[at]math[dot]ucla[dot]edu

cladekl[at]math[dot]ucla[dot]edu

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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. Together with Polona Durcik, I am organizing the Caltech-UCLA joint analysis seminar.

Interests:
  • 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.

Research:
    Manuscripts in preparation:
  • A discrete Stein-Wainger theorem with a restricted supremum (with Ben Krause and Michael Lacey).
  • Sums and products for porous measures.
  • Spherical means on the Heisenberg group: stability of a maximal function estimate (with Theresa Anderson, Malabika Pramanik, and Andreas Seeger).
  • Submitted and/or published articles:
  • Sparse bounds for pseudodifferential operators (with David Beltran). arXiv
    Preprint.
  • Sparse domination of Hlbert transforms along curves (with Yumeng Ou). arXiv
    Math. Res. Lett., to appear
  • Improved endpoint bounds for the lacunary spherical maximal operator (with Ben Krause). arXiv
    Preprint.
  • Radial Fourier Multiplers in R3 and R4. arXiv
    Anal. PDE.
  • A discrete Carleson theorem along the primes with a restricted supremum (with Kevin Henriot, Ben Krause, Izabella Laba and Malabika Pramanik). arXiv
    Math. Z., to appear.
  • On the square function associated with generalized Bochner-Riesz means arXiv
    Ind. Univ. Math. J., to appear.
  • New Lp bounds for Bochner-Riesz multipliers associated with convex planar domains with rough boundary. arXiv
    Preprint.
  • Multiplier transformations associated to convex domains in R2. arXiv
    J. Geom. Anal.
Any opinions, findings, and conclusions or recommendations expressed on this webpage are those of the author and do not necessarily reflect the views of the National Science Foundation.