My research topics in the past and present include
- Analysis of nonlinear diffusion systems and multiscale analysis of variational evolutions
- Kinetic equations: qualitative properties, multiscale modeling and analysis, and numerical simulation
- Optimal control with PDEs: multiscale analysis of adjoint-based methods
- Interacting particle systems: consensus-based methods in global optimization, disease and population dynamics, large deviations
- Variational methods and algorithms in quantum computing
My current focus lies on the connections between optimal transport, (generalized) gradient flows and large deviations, and on probabilistic methods for studying variational evolutions, with an eye toward applications.