Geometry | CMAFcIO

Geometric formulation of the calculus of variations, and of equations obtained from the application of a variational principle in mechanics, control or field theories,with recent results on the reduction of variational principles when the Lagrangian density is invariant with respect to a Lie group action.

The study of the existence of conserved quantities of constrained Willmore surfaces, both polynomial and of formal series type, and their geometrical interpretation.

Baecklund and Darboux transformations of contrained Willmore surfaces.

2) Singularity theory and D-Module theory:

Deformations of germs of Legendrian curves on a 3-dimensional contact manifold and its generalization to higher dimensions. Relation with D-Module theory, álgebras of deformation-quantization, perverse sheaves, holomorphic families of perverse sheaves, subanalytic geometry.