The local study of plane algebraic curves has an ancient history, but it 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 aim is to demonstrate a recent theorem that gives a complete description of the topology of singular points of real algebraic curves in the plane.

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

 

* Basic syllabus. The teacher has the autonomy to make any changes.