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

In my two talks, I will present the paper "BPS polynomials and Welschinger invariants" of Argüz and Bousseau which shows that the Block-Göttsche polynomials of a toric del Pezzo surface S compute the BPS polynomials of the product of S with P^1. From this, it is conjectured that more the Welschinger invariants of Blow-ups of P^2 can always be recovered by specializing the BPS polynomials, which is confirmed in some cases. The proof uses degenerations of the toric surface, after which both the BPS polynomials and the Welschinger invariants are related to counts of floor diagrams.

In my two talks, I will present the paper "BPS polynomials and Welschinger invariants" of Argüz and Bousseau which shows that the Block-Göttsche polynomials of a toric del Pezzo surface S compute the BPS polynomials of the product of S with P^1. From this, it is conjectured that more the Welschinger invariants of Blow-ups of P^2 can always be recovered by specializing the BPS polynomials, which is confirmed in some cases. The proof uses degenerations of the toric surface, after which both the BPS polynomials and the Welschinger invariants are related to counts of floor diagrams.

On parlera des invariants énumératifs raffinés définis via un dénombrement de courbes réelles.

In these 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 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).