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7th Workshop on Combinatorics of Moduli Spaces, Cluster Algebras, and Topological Recursion (MoSCATR VII)
May 31, 2021 16:00–17:00, HSE, MIAN, Skoltech, Moscow
 


Stable maps to Looijenga pairs

A. Brini

The University of Sheffield
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MP4 327.2 Mb

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Abstract: A Looijenga pair is a pair (X,D) with X a smooth complex projective surface and D a singular anticanonical divisor in X. I will describe a series of correspondences relating five different classes of string-theory motivated invariants specified by the geometry of (X,D):
  • the log Gromov–Witten theory of (X,D),
  • the Gromov–Witten theory of X twisted by the sum of the dual line bundles to the irreducible components of D,
  • the open Gromov–Witten theory of special 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.
I will also show how the problem of computing all these invariants is closed-form solvable. Joint work with P. Bousseau and M. van Garrel.

Language: English
 
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