Research Areas

My research focuses on applied mathematics and data science, with emphasis on developing efficient algorithms and theoretical frameworks for real-world problems. Below is an overview of my main research areas. For a comprehensive list of publications, please see my Papers page or Google Scholar profile.

Mathematics of AI and Learning Theory

I work on theoretical understanding of modern machine learning and artificial intelligence. My research addresses fundamental questions about why neural networks and other learning algorithms succeed in practice, including the phenomenon of benign overfitting where models can fit data perfectly yet still generalize well. This work bridges classical statistical learning theory and modern deep learning, providing rigorous mathematical analysis of neural network training dynamics, generalization bounds, and implicit regularization. Understanding these phenomena is critical for developing more robust and reliable AI systems.

Stochastic Optimization and Iterative Methods

I develop and analyze stochastic iterative methods for solving large-scale optimization problems and linear systems. This includes work on randomized Kaczmarz methods, stochastic gradient descent variants, and accelerated methods for non-convex problems. My research explores how randomization can improve convergence rates and scalability, with applications to high-dimensional data analysis, federated learning, and distributed computation.

Machine Learning and Fairness

My research in machine learning emphasizes transparency, interpretability, and fairness. I work on methods including non-negative matrix factorization and topic modeling that provide interpretable results while maintaining strong predictive performance. Recent work addresses fairness in machine learning, exploring how to build algorithms that provide equitable performance across different population groups. I'm also interested in theoretical foundations of learning and robust reconstruction from incomplete data.

Tensor Analysis and Factorization

Tensors (higher-dimensional arrays) appear naturally in many applications including imaging, genomics, and text analysis. My research develops algorithms for tensor decomposition, low-rank tensor recovery, and tensor-based regression. This includes extending sparse recovery and matrix factorization techniques to the tensor setting, as well as developing randomized methods for efficient tensor computations.

Applications with Community Partners

I'm committed to translating mathematical research into solutions for real-world problems. Recent collaborations include work with the Innocence Project on exoneree support and justice initiatives, applying data analysis techniques to improve outcomes for wrongfully convicted individuals. Additionally, I work with LymeDisease.org on statistical analysis and modeling of Lyme disease data to inform patient advocacy, research directions, and public health policy. These partnerships demonstrate the power of collaborative mathematical research in addressing urgent societal challenges.

Additional Interests

Recent work explores connections between numerical methods and machine learning, manifold learning, phase retrieval problems, and applications to medical data analysis. I'm particularly interested in translating theoretical advances into practical algorithms that solve real-world problems with tangible impact.