Singular points of planar real analytic curves
Etienne Ghys

The topological nature of singular points of planar complex analytic curves has been understood for many years. Indeed, Newton-Puiseux series allow a complete understanding of the link of the singularity. Amazingly, the analogous question in the real domain leads to interesting combinatorical developments. I will start my discussion with a clever remark of M. Kontsevich.