Summary of Research Interests
-Uncertainty quantification
Nonstationary Baysian inverse problems
Statistical models and optimal transportation
Sampling, Markov chain Monte Carlo methods
Data assimilation, filtering and smoothing algorithms
-Geophysical Fluid Dynamics
Hamiltonian Particle-Mesh Methods for the Shallow-Water Equations
Semi-Implicit and Staggered Semi-Lagrangian Methods for the
Shallow-Water Equations
Geostrophic Balance and Asymptotic Analysis
Non-hydrostatic motion and numerical methods
Multi-symplectic Structure and Conservation of Potential Vorticity
Data assimilation and ensemble Kalman filters
-Molecular Dynamics
Particle Methods and Statistical Mechanics
Time stepping methods for classical, stochastic and quantum-classical
molecular dynamics Hybrid Monte Carlo methods
-Geometric Integration
Hamiltonian ODEs and PDEs
Computation of Lyapunov Exponents
Backward Error Analysis
Adaptivity and Conservation
-Averaging in highly oscillatory systems and general multi-scale analysis
Existence and life-span of adiabatic invariants
Large time-step numerical methods
Mori-Zwanzig reduction and stochastic modelling