Groupes de travail : Groupe de travail Invariants énumératifs raffinés et invariants à valeurs dans des modules skein

In these two talks I will introduce Pierrick Bousseau's work on a relationship between some Gromov-Witten invariants of a toric surface and the Block-Göttsche invariants which were defined in Ilia's talk. When the toric surface satisfies the so-called "h-transversality" condition, the invariants are more easily defined: I will focus on this case. On the tropical side, it amounts to consider particular configurations of points which are "vertically stretched". The corresponding tropical curves split into "floor diagrams": I will explained what those are, and how the Block-Göttsche invariants can be computed in this situation. If time permits, I will already sketch the structure of Bousseau's argument.

In these two talks I will introduce Pierrick Bousseau's work on a relationship between some Gromov-Witten invariants of a toric surface and the Block-Göttsche invariants which were defined in Ilia's talk. When the toric surface satisfies the so-called "h-transversality" condition, the invariants are more easily defined: I will focus on this case. On the tropical side, it amounts to consider particular configurations of points which are "vertically stretched". The corresponding tropical curves split into "floor diagrams": I will explained what those are, and how the Block-Göttsche invariants can be computed in this situation. If time permits, I will already sketch the structure of Bousseau's argument.

In my talks, I will give an introduction to the theory of skein-valued open Gromov-Witten invariants of Ekholm and Shende. In the first talk, I will discuss the basic definitions of the theory and a couple of examples. In particular, I will explain how the skein relations arise naturally from the possible degenerations of bordered holomorphic curves.

In my talks, I will give an introduction to the theory of skein-valued open Gromov-Witten invariants of Ekholm and Shende. In the first talk, I will discuss the basic definitions of the theory and a couple of examples. In particular, I will explain how the skein relations arise naturally from the possible degenerations of bordered holomorphic curves.

La première séance du groupe de travail sera consacrée à deux approches aux invariants énumératifs raffinés :  l'approche tropicale (F. Block et L. Göttsche) et celle via un dénombrement de courbes réelles (G. Mikhalkin).