The differential geometry of starfish cycles: A 20-year retrospective and open problems

After a discussion of “starfish politics” a survey of starfish outbreak models of the late 1980s is given. The role of differential geometry of the production of reef skeletons, originally used merely as a parameter reduction method for these many-parameter models, is shown to have evolved into a fundamental method for modelling social structures and guilds. This, in turn, has spurred the development of Finsler diffusions and noise, as it is the Finsler geometries of reef production which encode these social structures. Finsler filtering problems are discussed and several open problems are stated.