Diana Chua Halikias

Welcome! I am a PhD candidate in math at Cornell University. My advisor is Alex Townsend.
I study numerical analysis and am especially interested in randomized linear algebra, matrix theory, and PDE learning.
I am currently applying to postdocs.

In the summer of 2024, I interned in the Center for Computational Mathematics at the Flatiron Institute and worked with Lawrence Saul. Previously, I interned in the Machine Learning and Analytics group run by Michael Mahoney at Lawrence Berkeley National Laboratory.
Before Cornell, I completed my undergraduate degree in math at Yale.
My CV is here. You can email me at dh736 at cornell dot edu.

Research

I am fortunate to be supported by the NSF-GRFP.

  • Near-optimal hierarchical matrix approximation from matrix-vector products
    with Tyler Chen, Feyza Duman Keles, Cameron Musco, Christopher Musco, and David Persson, accepted to SODA 2025 (2024). (arxiv).
  • Fixed-sparsity matrix approximation from matrix-vector products
    with Noah Amsel, Tyler Chen, Feyza Duman Keles, Cameron Musco, and Christopher Musco, preprint (2024). (arxiv).
  • Operator learning without the adjoint
    with Nicolas Boullé, Samuel Otto, and Alex Townsend, to appear in J. Mach. Learn. Res. (2024). (arxiv).
  • Elliptic PDE learning is provably data-efficient
    with Nicolas Boullé and Alex Townsend, PNAS Brief Report Vol. 120, no. 39, (2023). (journal, arxiv).
  • Structured matrix recovery from matrix-vector products
    with Alex Townsend, Numer Linear Algebra Appl. e2531, (2023). (journal, arxiv).
  • Arbitrary depth universal approximation theorems for operator neural networks
    with Annan Yu, Chloé Becquey, Matthew Mallory and Alex Townsend, preprint. (arxiv)
  • Discrete variants of Brunn-Minkowski type inequalities
    with Bo'az Klartag and Boaz Slomka, Ann. Fac. Sci. Toulouse Math. (6), Vol. 30, no. 2, (2021), 267-279. (journal, arxiv).
  • A Cheeger inequality for graphs based on a reflection principle
    with Ed Gelernt, Charlie Kenney, and Nicholas Marshall, Involve 13 no. 3, (2020) 475-486 (journal, arxiv).

    • Outreach

  • I run a Little Math Circle for children in grades K-5 in the Ithaca area.
  • I mentored a research project on the theoretical aspects of machine learning as part of the 2021 Cornell REU.
  • I have mentored two directed reading projects with Cornell undergraduates on spectral graph theory.

    • Miscellaneous

    I am the trivia host at Cornell's graduate weekly trivia night at the Big Red Barn!
    I also love rock climbing and playing piano.
    At Yale, I worked for three years in the Numismatics department of the Yale University Art Gallery.