Cactus groups and plane curves (en distanciel)

Cactus groups are related to the moduli spaces of stable real rational curves with marked points; the pure cactus groups are the fundamental groups of these spaces. Elements of cactus groups can be represented by some kind of planar braids and I will talk about various consequences of this fact. In particular, I will describe the "closures" of such braids and discuss their relation to the theory of immersed curves without triple self-intersections (aka doodles).