Space based microlensing planet searches

The discovery of extra-solar planets is arguably the most exciting development in astrophysics during the past 15 years, rivalled only by the detection of dark energy. Two projects unite the communities of exoplanet scientists and cosmologists: the proposed ESA M class mission EUCLID and the large space mission WFIRST, top ranked by the Astronomy 2010 Decadal Survey report. The later states that: "Space-based microlensing is the optimal approach to providing a true statistical census of planetary systems in the Galaxy, over a range of likely semi-major axes". They also add: "This census, combined with that made by the Kepler mission, will determine how common Earth-like planets are over a wide range of orbital parameters". We will present a status report of the results obtained by microlensing on exoplanets and the new objectives of the next generation of ground based wide field imager networks. We will finally discuss the fantastic prospect offered by space based microlensing at the horizon 2020-2025.Comment: 8 pages, Proceedings to the ROPACS meeting "Hot Planets and Cool Stars" (Nov. 2012, Garching), invited contributio

Explicit minimal Scherk saddle towers of arbitrary even genera in R3\R^3

Starting from works by Scherk (1835) and by Enneper-Weierstra\ss \ (1863), new minimal surfaces with Scherk ends were found only in 1988 by Karcher (see \cite{Karcher1,Karcher}). In the singly periodic case, Karcher's examples of positive genera had been unique until Traizet obtained new ones in 1996 (see \cite{Traizet}). However, Traizet's construction is implicit and excludes {\it towers}, namely the desingularisation of more than two concurrent planes. Then, new explicit towers were found only in 2006 by Martin and Ramos Batista (see \cite{Martin}), all of them with genus one. For genus two, the first such towers were constructed in 2010 (see \cite{Valerio2}). Back to 2009, implicit towers of arbitrary genera were found in \cite{HMM}. In our present work we obtain {\it explicit} minimal Scherk saddle towers, for any given genus $2k$, $k\ge3$