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It is well known that the solar gravitational field can be considered as a telescope with a prime focus at locations beyond 550 au. In this work we present a new derivation of the wave-optical properties of the system, by adapting the arrival-time formalism from gravitational lensing. At the diffraction limit the angular resolution is similar to that of a notional telescope with the diameter of the Sun, and the maximum light amplification is $8{\pi}4GM /(c^2{\lambda})$, enough to detect a 1 W laser on Proxima Centauri b pointed in the general direction of the Sun. Extended sources, however, would be blurred by the wings of the point spread function into the geometrical-optics regime of gravitational lensing. Broad-band sources would have to further contend with the solar corona. Imaging an exoplanet surface as advocated in the literature, without attempting to reach the diffraction limit, appears achievable. For diffraction-limited imaging (sub-km scales from 100 pc) nearby neutron stars appear to be most plausible targets.

Let D be a holomorphic differential operator acting on sections of a holomorphic vector bundle on an n-dimensional compact complex manifold. We prove a formula, conjectured by Feigin and Shoikhet, for the Lefschetz number of D as the integral over the manifold of a differential form. The class of this differential form is obtained via formal differential geometry from the canonical generator of the Hochschild cohomology of the algebra of differential operators in a formal neighbourhood of a point. If D is the identity, the formula reduces to the Riemann--Roch--Hirzebruch formula., Comment: 31 pages, 1 figure. Misprints corrected and appendix with analytical details added in v3

We quantize the Poisson-Lie group SL(2,R)^* as a bialgebra using the product of Kontsevich. The coproduct is a deformation of the coproduct that comes from the group structure. The resulting bialgebra structure is isomorphic to the quantum universal enveloping algebra U_hsl(2,R)., Comment: 11 pages, 2 figures, LaTeX2e