LRI Research Programme

Variational Geometry

  • Integral variational functionals on fibred manifolds and Grassmann fibrations
  • Variational sequences and applications, generalisations, bicomplexes
  • Variational control theory
  • Variational partial differential equations
  • Symmetries of variational functionals and differential equations
  • The inverse problem of the calculus of variations, Helmholtz conditions and generalisations
  • The Sonin-Douglas problem

Geometric Mechanics

  • Constraints
  • Variational forces
  • Ostrogradsky (higher order) mechanics
  • Symmetries and conservation laws, Hamilton structures, recursion operators

Extensions of Riemannian Geometry

  • Finsler structures and generalisations
  • Kawaguchi spaces

Nonlinear Partial Differential Equations

  • Symmetries and conservation laws
  • Integrable systems
  • Computer algebra tools for computations

Variational principles in classical field theory

  • Jet structures and differential invariants
  • Higher order velocities and Grassmann fibrations, flag fibrations
  • Variational foundations of the general relativity theory
  • Natural Lagrange structures
  • Energy-momentum tensors