Deformations of coisotropic submanifolds for fibrewise entire Poisson structures

We show that deformations of a coisotropic submanifold inside a fibrewise entire Poisson manifold are controlled by the $L_\infty$-algebra introduced by Oh-Park (for symplectic manifolds) and Cattaneo-Felder. In the symplectic case, we recover results previously obtained by Oh-Park. Moreover we consider the extended deformation problem and prove its obstructedness

Interstellar Scattering Towards the Galactic Center as Probed by OH/IR Stars

Angular broadening measurements are reported of 20 OH/IR stars near the galactic center. This class of sources is known to have bright, intrinsically compact (less than or equal to 20 mas) maser components within their circumstellar shells. VLBA antennas and the VLA were used to perform a MKII spectral line VLBI experiment. The rapid drop in correlated flux with increasing baseline, especially for sources closest to the galactic center, is attributed to interstellar scattering. Angular diameters were measured for 13 of our sources. Lower limits were obtained for the remaining seven. With the data, together with additional data taken from the literature, the distribution was determined of interstellar scattering toward the galactic center. A region was found of pronounced scattering nearly centered on SgrA*. Two interpretations are considered for the enhanced scattering. One hypothesis is that the scattering is due to a clump of enhanced turbulence, such as those that lie along lines of sight to other known objects, that has no physical relationship to the galactic center. The other model considers the location of the enhanced scattering to arise in the galactic center itself. The physical implications of the models yield information on the nature of interstellar scattering

Quantized Heisenberg Space

We investigate the algebra $F_q(N)$ introduced by Faddeev, Reshetikhin and Takhadjian. In case $q$ is a primitive root of unity the degree, the center, and the set of irreducible representations are found. The Poisson structure is determined and the De Concini-Kac-Procesi Conjecture is proved for this case. In the case of $q$ generic, the primitive ideals are described. A related algebra studied by Oh is also treated.Comment: 20 pages LaTeX documen

Exact Lagrangian submanifolds, Lagrangian spectral invariants and Aubry-Mather theory

We construct graph selectors for compact exact Lagrangians in the cotangent bundle of an orientable, closed manifold. The construction combines Lagrangian spectral invariants developed by Oh and results by Abouzaid about the Fukaya category of a cotangent bundle. We also introduce the notion of Lipschitz-exact Lagrangians and prove that these admit an appropriate generalization of graph selector. We then, following Bernard-Oliveira dos Santos, use these results to give a new characterization of the Aubry and Mane sets of a Tonelli Hamiltonian and to generalize a result of Arnaud on Lagrangians invariant under the flow of such Hamiltonians.Comment: v4: final version; to appear in Math. Proc. Camb. Phil. So