We consider differential operators between sections of arbitrary powers of the determinant line bundle over a contact manifold. We extend the standard notions of the Heisenberg calculus:â€¦ (More)

The pentagram map is a projectively natural transformation defined on (twisted) polygons. A twisted polygon is a map from Z into RP that is periodic modulo a projective transformation called theâ€¦ (More)

We prove the existence and the uniqueness of a conformally equivariant symbol calculus and quantization on any conformally flat pseudo-Riemannian manifold (M, g). In other words, we establish aâ€¦ (More)

The spaces of linear differential operators D Î» (R n) acting on Î»-densities on R n and the space Pol(T * R n) of functions on T * R n which are polynomial on the fibers are not isomorphic as modulesâ€¦ (More)

We study deformations of the standard embedding of the Lie algebra Vect(S 1) of smooth vector fields on the circle, into the Lie algebra of functions on the cotangent bundle T * S 1 (with respect toâ€¦ (More)

Let M be a smooth manifold, S the space of polynomial on fibers functions on T * M (i.e., of symmetric contravariant tensor fields). We compute the first cohomology space of the Lie algebra, Vect(M),â€¦ (More)

We classify non-trivial (non-central) extensions of the group Diff(S1) of all diffeomorphisms of the circle preserving its orientation and of the Lie algebra Vect(S1) of vector fields on S1, by theâ€¦ (More)

Let Dk be the space of k-th order linear differential operators on R: A = ak(x) d dx + Â· Â· Â· + a0(x). We study a natural 1-parameter family of Diff(R)(and Vect(R))-modules on Dk. (To define thisâ€¦ (More)

We classify nontrivial deformations of the standard embedding of the Lie algebra Vect(S1) of smooth vector fields on the circle, into the Lie algebra Î¨D(S1) of pseudodifferential symbols on S1. Thisâ€¦ (More)

We consider a Lie algebra generalizing the Virasoro algebra to the case of two space variables. We study its coadjoint representation and calculate the corresponding Euler equations. In particular,â€¦ (More)