Résumé :
The zero set of the function "altitude" on our spherical earth is precisely the coast line. We can imagine it to be a random collection of curves, which evolves in time according to tectonic principles. Most of the time, the coast deforms in place, but sometimes the topology changes, for instance when an underwater volcano becomes an island, or when the meander of a river becomes a cutoff.
We will introduce random objects (collections of curves, surfaces...) that evolve in similar ways, and try to understand how their topology evolves. Here are some questions one can ponder: does the coast line become increasingly complex? do we see an accumulation of islands into lakes into islands into lakes? can any collection of curve in space appear in this model? if so, how do we force their apparition? In my time, I hope to guide you through this unexplored landscape.
