# Topological algorithms for graphs on surfaces

Given a "topologically interesting" surface (up to homeomorphism, a sphere with handles -- for example, the surface of a pretzel), how can we cut it to make it planar (homeomorphic to a disk)? How to compute a shortest non-contractible closed curve on a surface (which cannot be continuously shrunk to a point while staying on the surface)? How to tighten as much as possible a closed curve on a surface by deformation (homotopy)?

The aim of this talk is to survey techniques for solving such topological problems, which belong to the recent field of computational topology and have connections with topological graph theory and graph algorithms. These questions are also motivated by applications in computer graphics and geometric modelling, where parameterizing or simplifying a surface mesh is useful in several contexts.

The talk will be self-contained; in particular, no prior exposure to algorithms is necessary.