Research Overview

My primary research interests lie at the intersection of machine learning, applied probability, and dynamical systems. My research portfolio spans a diverse set of interconnected topics, ranging from foundational theory to algorithmic development and scientific applications. While much of my work is motivated by foundational questions, it is often closely connected to implementation challenges and a broad spectrum of practical applications across the sciences.

Main topics of interest include:

• Generative modeling: develop and analyze dynamical measure transport methods for generative modeling, including applications to sequential data
• Sequence modeling: develop and analyze mathematically grounded methods for modeling and learning from sequential data
• Optimization and sampling: analyze and improve optimization and sampling methods in ML through principled mathematical approaches
• Robustness and reliability: develop and analyze probabilistic methods to make ML systems more robust and more reliable
• Stochastic differential equations (SDEs): analyze SDEs with multiple time scales through homogenization and stochastic analysis, with applications to statistical mechanics and data-driven inference of effective dynamics

Outside of these topics, I maintain a broad interest in various topics at the interface of probability theory and mathematical physics; e.g., quantum stochastic calculus, rough paths theory, and concentration inequalities, among others.