As shown by recent gravitational wave detections, galaxies harbour an unknown population of black holes at high masses. In our Galaxy such dark objects can be found and studied solely via gravitational microlensing methods. This paper described our search for black-hole lenses both in archived OGLE data and among on-going microlensing events found by OGLE and Gaia. That combination of superb time-domain astrometry and photometry will enable us to derive masses and distances to these dark lenses uniquely, and to describe the demographics of the unseen component of the Milky Way.

Gaia will see little of the Galactic mid-plane and nuclear bulge due to high extinction at optical wavelengths. To study the structure and kinematics of the inner Galaxy we must look to longer wavelengths. The Vista Variables in the Via Lactea (VVV, Minniti et al. 2010) survey currently provides just over 4 years of observations covering approximately 560 square degrees of the Galactic bulge and plane. Typically each source is observed 50–150 times in the Ks band over this period. Using these data we provide relative proper motions for approximately 200 million unique sources down to Ks∼16 with uncertainties approaching 1 mas yr−1. In addition, we fit a solution of the parallactic motion of all sources with significant proper motion and discover a number of new nearby brown dwarfs. These results will allow us to identify faint common proper motion companions to stars with Gaia parallaxes, increasing the number of brown dwarf benchmark objects. Our absolute astrometric calibration precision is currently ∼ 2 mas yr−1, based on PPMXL. The Gaia absolute astrometric reference grid will allow us to precisely anchor our results and measure the streaming motions of stars in the bulge. Finally, we anticipate that the catalogue could provide kinematic distances to the numerous optically invisible high amplitude variable stars that VVV is discovering.

Metallicity may play an important role in the symbiotic phenomenon. Unfortunately, chemical abundances of symbiotic stars have been thus far poorly studied. Ongoing abundance analysis of a sample of over 30 symbiotic stars based on high-resolution, near-infrared spectra obtained with the Phoenix spectrometer on Gemini South telescope will allow for the first time to address properly the metallicity problem as well as provide important information about the past history of these binaries.

We study compact Riemann surfaces of genus $g\geq2$ having a dihedral group of automorphisms. We find necessary and sufficient conditions on the signature of a Fuchsian group for it to admit a surface kernel epimorphism onto the dihedral group $D_N$. The question of extendability of the action of $D_N$ is considered. We also give an explicit parametrization of the moduli space of Riemann surfaces with maximal dihedral symmetry, showing that it is a one-dimensional complex manifold. Defining equations of all such surfaces and the formulae of their automorphisms are calculated. The locus of this moduli space consisting of those surfaces admitting some real structure is determined.

Two projective nonsingular complex algebraic curves X and Y defined over the field R of real numbers can be isomorphic while their sets X(R) and Y(R) of R-rational points could be even non homeomorphic. This leads to the count of the number of real forms of a complex algebraic curve X, that is, those nonisomorphic real algebraic curves whose complexifications are isomorphic to X. In this paper we compute, as a function of genus, the maximum number of such real forms that a complex algebraic curve admits.