This is an announcement for the paper "Complex structures on twisted Hilbert spaces" by Jesus M. F. Castillo, Wilson Cuellar, Valentin Ferenczi, and Yolanda Moreno. Abstract: We investigate complex structures on twisted Hilbert spaces, with special attention paid to the Kalton-Peck $Z_2$ space and to the hyperplane problem. We consider (nontrivial) twisted Hilbert spaces generated by centralizers obtained from an interpolation scale of K\"othe function spaces. We show there are always complex structures on the Hilbert space that cannot be extended to the twisted Hilbert space. If, however, the scale is formed by rearrangement invariant K\"othe function spaces then there are complex structures on it that can be extended to a complex structure of the twisted Hilbert space. Regarding the hyperplane problem we show that no complex structure on $\ell_2$ can be extended to a complex structure on an hyperplane of $Z_2$ containing it. Archive classification: math.FA Submitted from: castillo@unex.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1511.05867 or http://arXiv.org/abs/1511.05867