0000000000358856
AUTHOR
Mauricio Garay
showing 4 related works from this author
On simple families of functions and their Legendrian mappings
2004
We study germs of $n$-parameter families of functions, that is, function-germs of the type $f : (\mathbb{R}^n \times \mathbb{R}, 0) \to (\mathbb{R}, 0)$ defined on the total space of the trivial bundle $ \mathbb{R}^n \times \mathbb{R} \to \mathbb{R}^n $. There is a natural notion of $V$-equivalence for such function-germs. We introduce the Young diagram of $n$-parameter families satisfying a non-degeneracy condition. We classify all such simple $n$-parameter families and give their versal deformations. This result has direct applications to contact and projective geometry.
Resurgent Deformation Quantisation
2013
We construct a version of the complex Heisenberg algebra based on the idea of endless analytic continuation. In particular, we exhibit an integral formula for the product of resurgent operators with algebraic singularities. This algebra would be large enough to capture quantum effects that escape ordinary formal deformation quantisation.
Stable moment mappings and singular lagrangian Fibrations
2005
We study singular Lagrangian fibrations given by moment mappings using cohomological methods. We give a theorem for the stability of these foliations and construct a symplectic version of Mather’s stable mapping theorem.
A rigidity theorem for Lagrangian deformations
2005
We consider deformations of singular Lagrangian varieties in symplectic manifolds. We prove that a Lagrangian deformation of a Lagrangian complete intersection is analytically rigid provided that this is the case infinitesimally. This result is given as a consequence of the coherence of the direct image sheaves of relative infinitesimal Lagrangian deformations.