zkli[at]math.wisc.edu

I am a RTG Postdoctoral Fellow at the University of Wisconsin-Madison. I received my PhD from UCLA, where I was advised by Terence Tao.

My research is supported by NSF DMS-2154531. Here is my CV.

For a list of recordings and slides from my talks, click here.

I am a co-organizer of the Online Analysis Research Seminar.

Papers
  • An introduction to decoupling and harmonic analysis over Q_p. arXiv
    Expository paper, submitted.
  • A decoupling interpretation of an old argument for Vinogradov's Mean Value Theorem. arXiv
    (with Brian Cook, Kevin Hughes, Akshat Mudgal, Olivier Robert, and Po-Lam Yung)
    Submitted.
  • Improved discrete restriction for the parabola. arXiv
    (with Shaoming Guo and Po-Lam Yung)
    to appear in Mathematical Research Letters.
  • Decoupling for fractal subsets of the parabola. arXiv
    (with Alan Chang, Jaume de Dios Pont, Rachel Greenfeld, Asgar Jamneshan, and Jose Madrid) journal
    Mathematische Zeitschrift 301 (2022), 1851–1879.
  • A short proof of l^2 decoupling for the moment curve. arXiv
    (with Shaoming Guo, Po-Lam Yung, and Pavel Zorin-Kranich) journal
    American Journal of Mathematics 143 (2021), no. 6, 1983–1998.
  • A bilinear proof of decoupling for the cubic moment curve. arXiv
    (with Shaoming Guo and Po-Lam Yung) journal
    Transactions of the American Mathematical Society, 374 (2021), no. 8, 5405–5432.
  • An l^2 decoupling interpretation of efficient congruencing: the parabola. arXiv
    Revista Matematica Iberoamericana, 37 (2021), no. 5, 1761–1802. journal
  • Effective l^2 decoupling for the parabola. arXiv
    (with an appendix joint with Jean Bourgain) journal
    Mathematika 66 (2020), no. 3, 681–712.
  • Decoupling for the parabola and connections to efficient congruencing. url
    PhD Thesis, 2019.
  • Quadratic twists of elliptic curves with 3-Selmer rank 1. arXiv
    International Journal of Number Theory, 10 (2014), no. 5, 1191–1217. journal
  • Elliptic curves with full 2-torsion and maximal adelic Galois representations. arXiv
    (with David Corwin, Tony Feng, and Sarah Trebat-Leder) journal
    Mathematics of Computation, 83 (2014), no. 290, 2925–2591.
  • Arithmetic properties of Picard-Fuchs equations and holonomic recurrences. arXiv
    (with Alexander W. Walker) journal
    Journal of Number Theory, 133 (2013), no. 8, 2770–2793.
  • A normal form for cubic surfaces. journal
    International Journal of Algebra, 4 (2010), no. 5, 233–239.
  • On a special case of the intersection of quadric and cubic surfaces. journal
    Journal of Pure and Applied Algebra, 214 (2010), no. 11, 2078–2086.
  • Counting powers of words in monoids. journal
    (with Stephen P. Humphries)
    European Journal of Combinatorics, 30 (2009), no. 5, 1297–1308.