I will describe the history of the homotopy groups of spheres, and some of the many different roles they have come to play in mathematics.
The lecture will describe two variants of thin film flows, one involving wetting and the other involving evaporation. First, describing the spreading of mostly wetting liquid droplets on surfaces decorated with assemblies of micron-size cylindrical posts arranged in regular arrays. A variety of deterministic final shapes of the spreading droplets are obtained, including octagons, squares, hexagons and cricles. Dynamic considerations provide a "shape" diagram and suggest rules for control. It is then shown how these ideas can be used to explore (and control) splashing and to create polygonal hydraulic jumps. Second, the evaporation of volatile liquid drops is considered. Using experiments and theory it is shown how the sense of the internal circulation depends on the ratio of the liquid and substrate conductivities. The internal motions control the deposition patterns and so may impact various printing processes. These ideas are then applied to colloid deposition porous media.