Fields of Interest

  • Integrability of equations  in Fluid Dynamics: Reciprocal Methods, hodograph transformations, symmetries and reduction. Other algorithmic methods: Singular manifold method.
  • Dynamical systems.
  • Solitons and their dynamics.
  • Derivation of Lax pairs and their associated Quantum Mechanical problems.
  • Geometric methods in Mathematical Physics.
  • Geometric structures. Symplectic, Presymplectic, Poisson, Dirac, Jacobi and Riemmanian Geometry.
  • Lie systems and geometric structures: Lie systems, Lie-Hamilton systems, Dirac-Lie systems and Jacobi-Lie systems.
  • Supersymmetry and Supermanifolds. Noncommutative geometry.
  • Applications of Geometry in General Relativity.
  • Finance Mathematics.
  • String theory and its geometric background.
  • Random matrices and Stochastic Dynamics.
  • Rational differential equations and isonomodromy deformations.
  • Control theory and Mechanics.
  • Theoretical Mechanics.
  • Cosmology and Celestial Mechanics.
  • Geometric Hamilton Jacobi theories.
  • Nonlinear phenoma: applications in biology and medical purposes.