Quantum geometry of log-Calabi Yau surfaces

Andrea Brini (Sheffield)

28-Oct-2021, 09:00-10:00 (2 years ago)

Abstract: A log-Calabi Yau surface with maximal boundary, or Looijenga pair, is a pair (X,D) with X a smooth complex projective surface and D a singular anticanonical divisor in X. I will introduce a series of physics-motivated correspondences relating five different classes of enumerative invariants of the pair (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. Based on joint works with P. Bousseau, M. van Garrel, and Y. Schueler.

algebraic geometrycombinatorics

Audience: researchers in the topic


Online Nottingham algebraic geometry seminar

Series comments: Online geometry seminar, typically held on Thursday. This seminar takes place online via Microsoft Teams on the Nottingham University "Algebraic Geometry" team.

For recordings of past talks, copies of the speaker's slides, or to be added to the Team, please visit the seminar homepage at: kasprzyk.work/seminars/ag.html

Organizers: Alexander Kasprzyk*, Johannes Hofscheier*, Erroxe Etxabarri Alberdi
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