Fields of Interest

  • Geometric methods in Mathematical Physics. Geometric structures. Symplectic, Presymplectic, Poisson, Dirac, Jacobi, Kähler cosymplectic, Nambu–Poisson, Nambu–Jacobi backgrounds and Riemmanian Geometry.
  • Lie systems and geometric structures.
  • Differential equations and their geometry.
  • Symmetry and Supersymmetry. Supermanifolds.
  • Applications of Geometry in General Relativity.
  • String theory and its geometric background.
  • Geometric Mechanics and Control Theory.
  • Celestial Mechanics.
  • Nonlinear phenoma: integrability of nonlinear PDEs.
  • Dynamical systems. KAM theory.
  • Solitons and  dynamics.
  • Quantum Operators: definition, domain, reduction.
  • Financial Mathematics
  • Material Evolution: geometric aspects through Lie groupoids, Multisymplectic backgrounds and Lie group symmetries and reduction.