|DATE||November 23 (Mon), 2020|
|SPEAKER||van Garrel, Michel|
|TITLE||Stable maps to Looijenga pairs|
|ABSTRACT||Let X be a smooth projective complex surface and let D be a reduced, singular anticanonical divisor in X whose irreducible components are all nef and smooth.
I will describe a series of correspondences relating five different classes of enumerative invariants specified by the geometry of (X,D): the log Gromov-Witten theory of the log Calabi-Yau pair (X,D); the twisted Gromov-Witten theory of the local Calabi-Yau surface given as the total space of the sum of the line bundles dual to the irreducible components of D; the open Gromov-Witten theory of toric Lagrangians in a toric Calabi--Yau 3-fold determined by (X,D); the Donaldson-Thomas theory of a symmetric quiver specified by (X,D); and a class of BPS invariants considered in different contexts by Klemm-Pandharipande, Ionel-Parker, and Labastida-Marino-Ooguri-Vafa. Moreover, these invariants turn out to be closed-form solvable.
This is joint work with Pierrick Bousseau (Paris Saclay) and Andrea Brini (Sheffield).