  Photometry of stars from the K2 extension of NASA's Kepler mission is
afflicted by systematic effects caused by small (few-pixel) drifts in the
telescope pointing and other spacecraft issues. We present a method for
searching K2 light curves for evidence of exoplanets by simultaneously fitting
for these systematics and the transit signals of interest. This method is more
computationally expensive than standard search algorithms but we demonstrate
that it can be efficiently implemented and used to discover transit signals. We
apply this method to the full Campaign 1 dataset and report a list of 36 planet
candidates transiting 31 stars, along with an analysis of the pipeline
performance and detection efficiency based on artificial signal injections and
recoveries. For all planet candidates, we present posterior distributions on
the properties of each system based strictly on the transit observables.
