Singularity Theory Topics: Combinatorics, Topology and Algebra

The local study of flat algebraic curves has an ancient history, but is still in constant development. This course aims to highlight some quite different aspects of the theory. A bit of classical algebra, with Newton’s polygon, a bit of topology, with Milnor’s fibration, and finally, a bit of combinatorics linked to graph theory. The goal is to come up with a recent theorem that gives a complete description of the topology of the singular points of real algebraic curves in the plane.

Reference:
Étienne Ghys: A singular mathematical promenade, prepublicação (2017).