Diana Chua Halikias

Welcome! I will be a Simons-Berkeley Research Fellow in the program on Complexity and Linear Algebra this coming fall. Starting in January 2026, I will be a Courant Instructor in the Department of Mathematics at NYU, where I will work primarily with Chris Musco. My research is broadly in numerical analysis and scientific machine learning. I am especially interested in randomized linear algebra, matrix theory, and operator learning. In May 2025, I graduated with a PhD in math from Cornell, where I was very fortunate to be advised by Alex Townsend.

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

  • Quasi-optimal hierarchically semi-separable matrix approximation
    with Tyler Chen, Feyza Duman Keles, Cameron Musco, Christopher Musco, and David Persson, preprint (2025). (arxiv).
  • Near-optimal hierarchical matrix approximation from matrix-vector products
    with Tyler Chen, Feyza Duman Keles, Cameron Musco, Christopher Musco, and David Persson, ACM-SIAM Symposium on Discrete Algorithms (2025). (journal, 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, J. Mach. Learn. Res. (2024). (journal, 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).

    • Teaching

    Cornell

  • Fall 2023: Math 2210 (Teaching Assistant)

    • Yale

  • Spring 2020: Math 231 (Peer Tutor)
  • Fall 2019: Math 230 (Peer Tutor)
  • Spring 2019: Math 244 (Peer Tutor)
  • Fall 2018: Math 115 (Peer Tutor)

    • Outreach

  • I ran 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 also mentored two directed reading projects with Cornell undergraduates on spectral graph theory.

    • Miscellaneous

    For three years, I was 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.