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Cette thèse traite d’algèbre et de géométrie algébrique, plus précisément de théorie algébrique des D-modules, avec une forte présence de la caractéristique positive. On sait le rôle joué par la...
Given a symplectic manifold (M; !) and a Lagrangian submanifold L, we construct versions of the symplectic blow-up and blow-down which are defined relative to L.
The recently proposed first-order parent formalism at the level of equations of motion is specialized to the case of Lagrangian systems. It is shown that for diffeomorphism-invariant theories the pare...
A symplectic bundle over an algebraic curve has a natural invariant sLag determined by the maximal degree of its Lagrangian subbundles. This can be viewed as a generalization of the classical Segre in...
We survey some of the state of the art regarding singu-larities in Lagrangian mean curvature ow. Some open problems are suggested at the end.
Given a Lagrangian sphere in a symplectic 4-manifold (M, ω) with b+ = 1, we find embedded symplectic surfaces intersecting it minimally. When the Kodaira dimension of (M, ω) is −∞, this result t...
The equation ∂2 ∂z∂¯z log(s2) = |Q|2s−4 + s2 (1.1) is satisfied by the conformally flat metric s2|dz|2 of a minimal Lagrangian surface in the complex hyperbolic plane CH2,...
This work originates from a heart’s images tracking which is to generate an apparent continuous motion, observable through intensity variation from one starting image to an ending one both supposed se...

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