On a sunny breezy day, sharp lines of light dance on the bottom of a swimming pool. They are due to folds - sometimes called 'caustics', or 'catastrophes' - in the wavefront of light from the Sun. Caustics also arise naturally in the distribution of dark matter in space. The dark matter density is very large at the location of a caustic. I'll show that the late infall of cold dark matter onto isolated galaxies, such as our own, produces discrete flows throughout the galactic halo, and associated caustics. One set of caustics are topological spheres surrounding the galaxy. Another set are rings in the galactic plane. Caustic rings are closed tubes whose cross-section is a D_{-4} catastrophe. I'll argue on theoretical and observational grounds that the caustic ring radii a_n (n=1,2,3..) obey the approximate law: a_n goes like 1/n. There is evidence for these rings in the distribution of bumps in the rotation curves of spiral galaxies, including our own Milky Way. The implications for dark matter searches will be discussed.
Luca Di Luzio
