Video library: A. Brini, Stable maps to Looijenga pairs

VIDEO LIBRARY


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

Stable maps to Looijenga pairs A. Brini The University of Sheffield
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