Analysis and Differential Equations

Research interests

  • Control theory, Hamilton-Jacobi-Bellman equations, Mean field games, Nonsmooth analysis.
  • Elliptic equations: nonlinear analysis and critical point theory, qualitative properties and symmetry of solutions, Liouville-type equations, Chern-Simons gauge theory.
  • Calculus of variations and geometric measure theory: Gamma-convergence, Homogenization, Fracture mechanics, Image processing, Analysis on fractals.
  • Geometric evolution equations: Mean curvature flow, Ricci flow.
  • Parabolic equations: convection-diffusion models, thin film equation, forward-backward equations, gradient flows.
  • Dynamical systems, Hamiltonian and Lagrangian systems: KAM Theory, weak KAM Theory, Aubry-Mather theory, Symplectic geometry.


Weekly Seminar