The interplay between Analysis, Probability, and Partial Differential Equations (PDEs) forms a crucial foundation for understanding a wide range of complex physical phenomena, including phase transitions, hydrodynamic and wave turbulence, and quantum field theory.
Areas of research interest include:
- Singular stochastic partial differential equations
- Navier-Stokes and Euler equations of incompressible fluids
- Fluid mixing
- Statistical mechanics
- Stochastic homogenization
- Wave and hydrodynamic turbulence
- Phase transitions and random media
- Kinetic theory
- General Relativity