Computing with real algebraic curves: topology and connectivity properties (Rémi Prébet)

Real algebraic curves arise in many applications, such as computer aided geometric design, geometric modeling, or robotics. They are also topical objects in computational real algebraic geometry, and an example of a basic task is that of computing the topology of such curves, embedded in an ambient space of a prescribed dimension. Besides, using the notion of roadmap, one can reduce connectivity queries in real algebraic sets of arbitrary dimensions to such queries in real algebraic curves. In this talk, I will give an overview of the main approaches to efficiently tackling these problems on real algebraic curves, depending on the dimension of the ambient space containing them. This contains joint work with Md. Nazrul Islam and Adrien Poteaux.