Marcos Cossarini

A wallsystem on a surface is a 1-submanifold satisfying certain conditions. It allows us to define a discrete notion of length and area: the length of a curve is the number of times that it crosses the wallsystem, and the area of the surface is the number of self-intersections of the wallsystem.  We will see how to approximate any Riemannian (or self-reverse Finsler) metric on a compact surface by a wallsystem, and we'll discuss applications to the filling area conjecture and the inverse problem for boundary distances.