Diana Halikias

Welcome! I am a Courant Instructor in the Department of Mathematics at NYU, where I work primarily with Chris Musco. Previously, I was a Simons-Berkeley Research Fellow in the program on Complexity and Linear Algebra. 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 diana.halikias at nyu dot edu.

Travel + Activities

Upcoming:

organizing a minisymposium on operator learning with Sam Otto at ILAS 2026 (5/18-5/22)
presenting at Workshop on Randomized Linear Algebra at EPFL (6/15-6/18)

Recently: spoke in Temple University's Applied + Computational Math seminar (4/22), Princeton's IdeAS seminar (3/19) and NYU's CMSC seminar (3/6); attended the 2026 Rising Stars in Computational & Data Sciences Workshop at the Santa Fe Institute (4/7-4/8) and the ICERM workshop on Randomized Numerical Linear Algebra (2/2-2/6). As part of the Simons program last semester, we organized a weekly seminar on Recent Progress and Open Directions in Matrix Computations !

Research

Attention Mechanisms Through the Lens of Numerical Methods: Approximation Methods and Alternative Formulations
with Michel Fabrice Serret, Alice Cortinovis, Yijun Dong, Anna Ma, Fabio Matti, Deanna Needell, Katherine J. Pearce, Elizaveta Rebrova, Disha Shur, Rudi Smith, Hai-Xiao Wang, and Laura Grigori , preprint (2026). (arxiv)
Fixed-sparsity matrix approximation from matrix-vector products
with Noah Amsel, Tyler Chen, Feyza Duman Keles, Cameron Musco, and Christopher Musco, SIAM J. Matrix Anal. Appl., (2026). (journal, arxiv)
Quasi-optimal hierarchically semi-separable matrix approximation
with Noah Amsel, Tyler Chen, Feyza Duman Keles, Cameron Musco, Christopher Musco, and David Persson, to appear in SIAM J. Matrix Anal. Appl., (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)
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

New York University

Spring 2026: Math UA-185 (Instructor)

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)

Diana Chua Halikias

Travel + Activities

Research

Teaching

Outreach

Miscellaneous