My research is broadly centred around PDEs with links to variational problems and probability, as well as applications in kinetic theory, statistical physics, material sciences and quantum mechanics. Quite often, very few and simple basic mechanisms can lead to a rich class of complex phenomena, whose description involves interesting mathematics. The projects I am working on are related to a series of current and highly active lines of research: optimal transportation, singular stochastic PDEs, Boltzmann equation, pattern formation problems, solitons. These diverse projects, though seemingly unconnected, upon closer inspection often share some common features:
- Ideas from regularity theory play a crucial role,
- nonlocal interactions are driving mechanisms,
- the analysis of continuum models is combined with probabilistic tools and thinking.
Variational methods for singular SPDEs
Calculus of variations
- Domain branching in micromagnetics and superconductivity
- Nonlocal Variational Problems related to Nonlinear Optics