- Statistical dynamics, McKean-Vlasov-Fokker-Planck equations. Global optimization, optimal control for PDEs and Machine Learning. Analysis, statistical inference and numerical methods for multiscale stochastic dynamical systems. Molecular dynamics and computational statistical mechanics.
- Global optimization, optimal control for PDEs, machine learning: Development and analysis of global optimization algorithms. Optimal control for agent-based models and for McKean-Vlasov PDEs. Applications to learning algorithms.
- Numerical Analysis and Statistical Inference: Parameter estimation for multiscale diffusions and for McKean SDEs.
- Markov Chain Monte Carlo: Development and analysis of accelerated sampling techniques. MCMC for multiscale probability measures. Computational statistical mechanics.
- Diffusion processes and stochastic differential equations: spectral theory for hypoelliptic operators, asymptotic problems for non-Markovian processes, averaging/homogenization for SDEs.
- Statistical mechanics: dynamical density functional theory, mean field limits for interacting diffusions, nonequilibrium statistical mechanics, kinetic theory and transport processes.