Research Interests

I work on the mathematical foundations of machine learning, with a particular focus on feature learning and optimization in neural networks. My research studies how the spectra and geometry of weights, gradients, and learned representations evolve during training—and how these dynamics shape implicit bias, generalization, and phase transitions in learning.

A central goal of my work is to develop a unified mathematical account of feature learning that connects finite-step optimization dynamics with asymptotic theories of wide neural networks. I am especially interested in identifying when training moves beyond fixed-feature or kernel-like behavior, how useful low-rank or heavy-tailed structure emerges, and how these phenomena depend on the data and optimization regime.

More broadly, I am interested in approximation theory, high-dimensional statistics, random matrix theory, and data geometry. I use these perspectives both to explain the behavior of existing learning algorithms and to guide the design of more principled optimization and learning methods.

Academic Background

• Assistant Professor of Mathematics, Boston College, 2024-present

• Hedrick Assistant Adjunct Professor, Department of Mathematics, University of California, Los Angeles, 2021-2024
  Mentors: Andrea Bertozzi, Jacob Foster, and Guido Montúfar

• Visiting Postdoctoral Researcher, Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany, 2022

• Visiting Assistant Researcher, Department of Statistics and Data Science, Yale University, 2020-2021

• Ph.D. in Applied and Interdisciplinary Mathematics, University of Michigan, 2021
  Advisors: Anna C. Gilbert and Raj Rao Nadakuditi

• B.S. with University Honors, Carnegie Mellon University, 2016
  Science and Humanities Scholars Program
  Majors: Mathematical Sciences (Discrete Mathematics and Logic) and Computer Science

Full CV

Talks 

Upcoming 

1. November 16–20, 2026 — Salt Lake City, Utah, for the SIAM Conference on Mathematics of Data Science (MDS26)

2. February 1–5, 2027 — IPAM, Los Angeles: co-organizing Algebraic Geometry: A Window to Machine Learning with Yulia Alexandr, Guido Montúfar, and Michael Murray

3. April 5–9, 2027 — ICERM, Providence: Sampling and Data in Algebraic Geometry, part of the Metric Algebraic Geometry semester program

Recent Past

4. June 2–5, 2026 — SIAM Conference on Optimization, Edinburgh: “Low Rank Gradients and Where to Find Them” 

5. June 2–5, 2026 — SIAM Conference on Optimization, Edinburgh: Organized the minisymposium Implicit Bias in Neural Network Optimization

6. March 8–13, 2026 — Mathematisches Forschungsinstitut Oberwolfach: co-organized the workshop Modern and Emerging Phenomena in Machine Learning

7. February 2026 — Brigham Young University seminar: “Implicit Bias of One Large Gradient Step”

8. November 2025 — University of Pittsburgh, Workshop on Analysis and Machine Learning: “Low Rank Gradients and Where to Find Them”

9. October 2025 — University of Massachusetts Lowell, Mathematics and Statistics Colloquium: “Universal Approximation Results for Solving PDEs with Neural Networks”

10. September 22–25, 2025 — Conference on Mathematics of Machine Learning, TU Hamburg: “Generalization with Non-Standard Spectra”

11. July 28–August 1, 2025 — SIAM Annual Meeting, Montréal: “Low Rank Structure and Double Descent,” minisymposium on double descent

12. July 2025 — ICML High-Dimensional Learning Theory Workshop: “Risk Phase Transitions in Spiked Regression,” oral presentation

13. May 2025 — UCLA Mathematics Colloquium: “Universal Approximation Results for Solving PDEs with Neural Networks”

14. April 2025 — Boston College Computer Science Seminar: “Implicit Bias of Gradient Descent: Spectral Dynamics and Generalization”

15. January 2025 — Eval Science Primer Series: “Generalization: Classical to Modern Regime”

16. January 2025 — Joint Mathematics Meetings, Seattle: “Supermodular Cone and Set-Function Optimization” 

17. January 2025 — Joint Mathematics Meetings, Seattle. Co-organized the session Geometry and Combinatorics in Deep Learning with Kathryn Lindsey and Eli Grigsby

18. December 16, 2024 — CFE-CMStatistics Conference, London, session on overparameterization in machine learning: “Double Descent and Benign Overfitting for Errors-in-Variables Regression”

19. November 4, 2024 — Tufts University, Computational and Applied Mathematics Seminar: “Universal Approximation Results for Solving PDEs with Neural Networks”

20. October 21–25, 2024 — SIAM Conference on Mathematics of Data Science, Atlanta: “Benign and Tempered Overfitting for Errors-in-Variables Regression with Low-Rank Data”

21. October 9, 2024 — Yale University, Applied Mathematics Seminar: “Universal Approximation Results for Solving PDEs with Neural Networks”

22. September 2024 — Florida State University, Applied and Computational Mathematics Seminar: “On Regularization via Early Stopping and Mini-Batching for Least Squares Regression”

23. September 2024 — IPAM Mathematics of Intelligences: tutorial on “Random Matrix Theory for Generalization”

24. September 9–December 13, 2024 — Long-term participant in IPAM’s Mathematics of Intelligences program, Los Angeles