This is an announcement for the paper "Complex intersection bodies" by A. Koldobsky, G. Paouris and M. Zymonopoulou. Abstract: We introduce complex intersection bodies and show that their properties and applications are similar to those of their real counterparts. In particular, we generalize Busemann's theorem to the complex case by proving that complex intersection bodies of symmetric complex convex bodies are also convex. Other results include stability in the complex Busemann-Petty problem for arbitrary measures and the corresponding hyperplane inequality for measures of complex intersection bodies. Archive classification: math.FA Submitted from: marisa.zym@gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1201.0437 or http://arXiv.org/abs/1201.0437