Estudio de invariantes enumerativas tropicales vía diagramas de pisos: crecimiento de la invariante quantum (2020)
The purpose of this degree project is to understand the asymptotic growth of the coefficients of the tropical enumerative invariant, known as the quantum invariant, as the degree of a tropical curve increases. For the above, we use floor diagrams which are, broadly speaking, connected and oriented graphs, considered as topological objects, which satisfy certain properties. The reason for using these objects is that they collect in them all the information of a tropical curve, so that they can be used to count the quantum invariant. More than that, they are simpler objects to understand, so that they simplify the calculation of the invariant. Thus, going from tropical curves to floor diagrams, only the combinatorial essence of the curves enumeration is preserved. And it is thanks to this construction and manipulating the floor diagrams with clever ideas, that the asymptotic growth of coefficients of the invariant quantum can be solved.