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Description

In this talk I will introduce the classical and tropical invariants corresponding to the enumeration of fixed genus (or cogenus) curves on a Surface, the floor diagrams, and their multiplicity in order to explicit some combinatorial aspects that allow us to establish the polynomiality property on the degree. I will explain how these polynomials can be seen as polynomials in two variables, the degree and the number of complex conjugated points of the configuration of points; and I will show some properties of the polynomials we obtain and some relations among them coming from known properties of the classical invariants. This is a joint work with E. Brugallé.