Research

My research interests broadly lie at the intersection of probability, statistics, and optimisation. I am interested in analyzing randomized algorithms in numerical linear algebra, machine learning, and data science, with a focus on developing theory and tools that allow us to better understand and work with large-scale or high-dimensional data.

Papers

• Subspace-constrained randomized coordinate descent for linear systems with good low-rank matrix approximations
  with Elizaveta Rebrova
  Preprint, 2025 [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
  To appear in Advances in Applied Probability, 2025+ [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

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

Presentations

• 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]