8 papers
Symplectic algebroids, groupoid Toeplitz operators and deformation quantization
Clément Cren, Jean-Marie Lescure, Omar Mohsen
We use Toeplitz operators to define a star-product on Poisson manifolds whose Poisson structure is induced by a symplectic Lie algebroid. The Toeplitz operators we consider are def…
Families of Toeplitz operators, family index and deformation quantization
Clément Cren, Erfan Rezaei
Given a contact fibration, we construct smooth families of Szegö projections on the fibers. This allows us to define smooth families of Toeplitz operators. We apply these operator…
Fields of Toeplitz algebras for the principal symbol of regular 2-step nilpotent groups
Clément Cren
We show that the C*-algebra of a regular 2-step nilpotent lie group can be recovered using continuous fields of Toeplitz algebras and a crossed product. We generalize this result t…
Stratification of the Helffer-Nourrigat cone
Clément Cren
Given a singular filtration on a manifold, e.g. a subriemannian setting, one can understand the elliptic regularity problems through a special kind of calculus. The principal symbo…
Filtered Calculus and crossed products by R-actions
Clément Cren
We show an isomorphism between the kernel of the C*-algebra of the tangent groupoid of a filtered manifold and the crossed product of the order 0 pseudodifferential operators in th…
Transverse parabolic structures and transverse BGG sequences
Clément Cren
Manifolds endowed with a parabolic geometry in the sense of Cartan come with natural sequences of differential operators and their analysis provide the so called (curved) BGG seque…