Research

My research is in computational mathematics, with a focus on randomised numerical methods. I am particularly interested in the design and analysis of efficient algorithms for large-scale computational problems, motivated by applications in data science, machine learning, and scientific computing. My work draws on ideas from numerical linear algebra, high-dimensional probability, and stochastic optimisation.

Papers

• Beyond Expectation: Concentration Inequalities for Randomized Iterative Methods
  with Toby Anderson, Max Collins, Jamie Haddock, and Elizaveta Rebrova
  Preprint, 2025 [arXiv]

• Subspace-constrained randomized coordinate descent for linear systems with good low-rank matrix approximations
  with Elizaveta Rebrova
  SIAM Journal on Matrix Analysis and Applications, vol. 47, no. 3, pp. 1495–1529, 2026 [journal] [arXiv]

• On Regularization via Early Stopping for Least Squares Regression
  with Rishi Sonthalia and Elizaveta Rebrova
  Preprint, 2024 [arXiv]

• Error dynamics of mini-batch gradient descent with random reshuffling for least squares regression
  with Rishi Sonthalia and Elizaveta Rebrova
  36th International Conference on Algorithmic Learning Theory (ALT 2025), 2025 [proceedings] [arXiv]

• On approximating the Potts Model with contracting Glauber dynamics
  with Roxanne He
  Advances in Applied Probability, vol. 58, no. 2, pp. 812–849, 2026 [journal] [arXiv]

• A subspace constrained randomized Kaczmarz method for structure or external knowledge exploitation
  with Elizaveta Rebrova
  Linear Algebra and its Applications, vol. 698, pp. 220–260, 2024 [journal] [arXiv]

Miscellaneous

• Randomized Iterative Algorithms in Numerical Linear Algebra
  PhD thesis [pdf]

• Markov chains, mixing times, and cutoff
  Undergraduate honours thesis [pdf]

Presentations

• Scientific Computing and Machine Learning Seminar, National University of Singapore: “Analysis of a randomly sparsified power method”, September 2026

• AMS Postdoc Seminar, Johns Hopkins University: “Subspace-constrained sketch-and-project solvers for linear systems with approximately low-rank structure or external knowledge”, April 2026 (virtual)

• ICERM Workshop on Randomized Numerical Linear Algebra, Providence, RI: “Subspace-constrained randomized coordinate descent for linear systems with good low-rank matrix approximations”, February 2026 [poster]

• Joint Mathematics Meetings (JMM 2026), Washington DC: “Efficient linear solvers for approximately low-rank linear systems”, January 2026

• Mid-Atlantic Numerical Analysis Day, Temple University: “Sketch-and-Project Solvers for Linear Systems with Low-Rank Structure”, November 2025

• Simons Institute Workshop on Linear Systems and Eigenvalue Problems, UC Berkeley: “Subspace-constrained randomized coordinate descent for linear systems with good low-rank matrix approximations”, October 2025 [poster]

• The Third Joint SIAM/CAIMS Annual Meetings (AN25), Montréal, Canada: “Subspace-constrained Sketch-and-project Solvers for Linear Systems with Low-rank Structure”, July 2025

• NLA group meeting, University of Oxford, UK: “Subspace-constrained sketch-and-project solvers for linear systems with low-rank structure”, July 2025

• The 36th International Conference on Algorithmic Learning Theory (ALT 2025), Milan, Italy: “Error dynamics of mini-batch gradient descent with random reshuffling for least squares regression”, February 2025

• Conference on the Mathematical Theory of Deep Neural Networks (DeepMath 2024), University of Pennsylvania, Philadelphia: “Error dynamics of mini-batch gradient descent with random reshuffling for least squares”, November 2024 [poster]

• CUNY Graduate Center Harmonic Analysis & PDE Seminar: “A subspace constrained randomized Kaczmarz method”, November 2024

• SIAM Conference on Mathematics of Data Science (MDS24), Atlanta: “A Subspace Constrained Randomized Kaczmarz Method for Structure or External Knowledge Exploitation”, October 2024 [poster]

• NSF CompMath PI Meeting, University of Washington, Seattle: “A Subspace Constrained Randomized Kaczmarz Method for Structure or External Knowledge Exploitation”, July 2024 [poster]