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
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
Differential Equations
Applications
- Computational mechanics and biomechanics
- Finite element method and isogeometric analysis
- Machine learning
