- Nonlinear and Stochastic Reduction: Markovian and non-Markovinan stochastic closures. Parameterizing manifolds and small-scale parameterizations in spatially extended systems. Ruelle-Pollicott resonances and reduced mixing spectrum.
- Random Dynamical Systems: Stochastic invariant manifolds and their numerical approximations. Random attractors and time-dependent invariant measures arising in dissipative stochastic systems.
- Data-Driven Stochastic Modeling: Data-adaptive harmonic spectra and multilayer Stuart-Landau models. Applications to Arctic sea ice modeling, and wind-driven ocean gyres.
- Optimal Control of Evolution Equations: Reduced-order models for the optimal control of PDEs and delay differential equations: analysis and computation.
- Geophysical Fluid Dynamics and Climate Dynamics: Natural climate variability. Low-order stochastic modelling of the El Niño-Southern Oscillation. Prediction of stochastic systems. Application of the geometric and ergodic theory of dynamical systems to climate dynamics.
Vimeo movie: https://vimeo.com/240039610