This is an announcement for the paper "Strictly convex norms and topology" by Jose Orihuela, Richard J. Smith, and Stanimir Troyanski. Abstract: We introduce a new topological property called (*) and the corresponding class of topological spaces, which includes spaces with $G_\delta$-diagonals and Gruenhage spaces. Using (*), we characterise those Banach spaces which admit equivalent strictly convex norms, and give an internal topological characterisation of those scattered compact spaces $K$, for which the dual Banach space $C(K)^*$ admits an equivalent strictly convex dual norm. We establish some relationships between (*) and other topological concepts, and the position of several well-known examples in this context. For instance, we show that $C(\mathcal{K})^*$ admits an equivalent strictly convex dual norm, where $\mathcal{K}$ is Kunen's compact space. Also, under the continuum hypothesis CH, we give an example of a compact scattered non-Gruenhage space having (*). Archive classification: math.FA math.GN Submitted from: richard.smith@ucd.ie The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1012.5595 or http://arXiv.org/abs/1012.5595