Research

Numerical analysis, probability, and mathematical physics.

My research focuses on the connection between interacting agent and particle systems and partial differential equations arising in computational problems, particularly sampling and optimization.

These two viewpoints complement each other. PDEs offer a macroscopic understanding of the dynamics, helping to address questions of stability, long-time behaviour, and convergence. Particle systems lead to efficient computational methods, often through Monte Carlo simulation, while also providing intuition about the underlying models. Propagation of chaos makes this connection precise in the many-particle limit.

Optimal transport is central to my work. I use its mathematical framework to understand and improve computational methods used by scientists and practitioners, with an emphasis on questions motivated by applications.

Current interests

• Collective training in machine learning.
• Variational inference via gradient flows.
• Monte Carlo methods for kinetic equations.

See my publications for individual papers.