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Seminars

Seminar
FIELD Mathematics
DATE November 23 (Mon), 2020
TIME 16:00-17:00
PLACE Online
SPEAKER van Garrel, Michel
HOST Oh, Jeongseok
INSTITUTE ETH
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).
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