Xiaorun Wu Home Page

Xiaorun Wu

Department of Mathematics
Columbia University
Room 509, MC 4406
2990 Broadway
New York, NY 10027
Email: xiaorunw at math dot columbia dot edu

About me

  • I am a second-year graduate student at Columbia University, expected to graduate in May 2027. My advisor is Professor Eric Urban. I obtained my undergraduate degree in May 2022 at Princeton University, under the supervision of Professor Shou-Wu Zhang and Professor Christopher Skinner.
  • My research interest is in number theory & arithmetic geometry. In particular, problems related to Iwasawa theory, automorphic forms and representations, Langlands program, and special values of L-functions, and applications in the context of Diophantine geometry: for example, BSD conjectures, and the existence of rational points in certain varieties.

  • Education

    Ph.D. in Mathematics   Columbia University   (Expected 2027).

    A.B. in Mathematics   Princeton University   (2018 - 2022).

    Research Publications

    My papers can also be found on arXiv here. (The papers may not reflect current research interests).

    Accepted for publication

    Higher moments for lattice point discrepancy of convex domains and annuli
    2021. Journal of Number Theory, accepted.
    arXiv Journal Talk by myself Abstract
    Given a domain \(\Omega \subseteq \mathbb R^2\), let \(\mathcal{D}(\Omega,x,R)\) be the number of lattice points from \( \mathbb Z^2\) in \(R\Omega -x\), for \(R \ge 1\) and \(x\in \mathbb T^2\), minus the area of \(R\Omega\): \[\mathcal{D}(\Omega,x,R) = \# \{ (j,k) \in \mathbb{Z}^2 :(j-x_1,k-x_2) \in R\Omega \} - R^2|\Omega|.\] We call \(\int_{\mathbb{T}^2}|\mathcal{D}(\Omega,x,R)|^pdx\) the \(p\)-th moment of the discrepancy function \(\mathcal{D}\). In 2014, Huxley showed that for convex domains with sufficiently smooth boundary, the fourth moment of \(\mathcal{D}\) is bounded by \(\mathcal{O}(R^2\log R)\), and in 2019, Colzani, Gariboldi, and Gigante extended this result to higher dimensions.

    In this paper, our contribution is twofold: first, we present a simple direct proof of Huxley's 2014 result; second, we establish new estimates for the \(p\)-th moments of lattice point discrepancy of annuli of radius \(R\), and any fixed thickness \(0< t<1\) for \(p\ge 2\).

    Honors and Awards

  • 2022 GSAS Fellowship, Columbia University
  • 2022 MAA Outstanding Presentation Award, Joint Mathematics Conference
  • 2021 MAA Outstanding Paper Award, Joint Mathematics Conference
  • 2018/2019 Putnam Competition Top 7% Contestants
  • 2015/2016 AIME Distinction, USAMO Qualifier
  • 2015 Gold Medal, Singapore Mathematical Olympiad (SMO).

  • Seminars Organized

  • 2023 Fall Diophantine Geometry Seminar
  • 2023 Spring Automorphic Forms & Representations Seminar
  • 2023 Spring \(p-\)adic Hodge Theory Seminar
  • 2022 Spring Princeton Univergraduate Student Seminar

  • Talks

  • Invited Speaker, AMS Contributed Paper Session for Graduate Student & Research Scholars on Algebraic and Arithmetic Geometry and Commutative Algebra, 2022, Seattle, WA [Program Link]
  • Poster Presenter, Joint Mathematics Conference, AMS-PME Student Poster Session, 2022, Seattle, WA [Program Link]
  • Poster Presenter, Mathematics Symposium, UIS, 2021, Chicago, IL [Poster]
  • Invited Speaker, Young Mathematician Conference, 2021, Columbus, OH [Slides]
  • Invited Speaker, MAA MathFest Student Paper Session, Virtual, 2021 [Abstract]
  • Invited Speaker, Brown University Symposium for Undergraduates in Mathematical Sciences (SUMS) , 2021, Virtual [Talk]
  • Invited Speaker, Joint Mathematics Conference, 2021, Virtual [Poster] [Talk]
  • Poster Presenter, Mathematics Symposium, UIS, 2020, Chicago, IL [Poster]
  • Invited Speaker, Young Mathematician Conference 2020, Columbus, OH [Slides]
  • Poster Presenter, Joint Mathematics Conference, Student Poster Session, 2020, Denver, CO [Poster]
  • Poster Presenter, Princeton SRC Conference, 2019, Princeton, NJ [Poster]

  • Teaching and Grading

  • MATH GU4042 Intro to Modern Algebra II, Fall 2023, Assistant Instructor.
  • MATH S3028 Partial Differential Equations, Summer II 2023, Assistant Instructor.
  • MATH S1012 Calculus II, Summer I 2023, Assistant Instructor.

  • See my contribution to Columbia Directed Reading Program .

    I am a member of Sigma Xi honor society, as well as a member of National Association of Mathematicians .

    Last updated on Sep 16, 2023