#### Enumerations of real curves

###### Autor: Erwan Brugallé Bouttier

###### Enumerative geometry is the area of mathematics which studies questions
like: how many lines pass through two points (easy)? How many conics
pass through five points (easy)? How many cubics with a crossing point
pass through 8 points (less easy)?
When dealing with algebraic curves defined over the field of complex
numbers, this number of curves does not depend on the chosen
configuration of points, in the same way that the number of roots of a
complex polynomial in one variable does not depend on its coefficients
but only on its degree. However, when dealing with algebraic curves
defined over the field of real numbers, this number heavily depends on
the chosen configurations of points, and the problem becomes much more
intricate. Recent years have seen a tremendous development in
enumeration of real curves, mainly based on the work by J.-Y. Welschinger.
In this talk, I will give an introduction to (real) enumerative geometry
and I will present some recent development in the field. I will in
particular make a detour via tropical geometry and tropical refined
invariants.