QK = GV for CY3 at g=0

Appears in collection : 2023 - T2 - WS2 - Higher structures in enumerative geometry

In this talk, I will show that on a Calabi-Yau threefold (CY3) a genus zero quantum K-invariant (QK) can be written as an integral linear combination of a finite number of Gopakumar–Vafa BPS invariants (GV) with coefficients from an explicit multiple cover formula. Conversely, all Gopakumar–Vafa invariants can be determined by a finite number of quantum K-invariants in a similar manner. The technical heart is a proof of a remarkable conjecture by Hans Jockers and Peter Mayr. This result is consistent with the “virtual Clemens conjecture” for the Calabi–Yau threefolds. A heuristic derivation of the relation between QK and GV via the virtual Clemens conjecture and a “multiple cover formula” will also be explained. This is a joint work with You-Cheng Chou.

Information about the video

Date of recording 12/06/2023
Date of publication 11/04/2024
Institution IHP
Licence CC BY-NC-ND
Language English
Audience Researchers, Graduate Students
Director(s) Alexandre Duplessis
Format MP4
Venue IHP - Hermite Amphitheater

Citation data

DOI 10.57987/IHP.2023.T2.WS2.003
Cite this video Lee, Yuan-Pin (12/06/2023). QK = GV for CY3 at g=0. IHP. Audiovisual resource. DOI: 10.57987/IHP.2023.T2.WS2.003
URL https://dx.doi.org/10.57987/IHP.2023.T2.WS2.003

Domain(s)

Algebraic Geometry

Bibliography

(Y.-C. Chou and Y.-P. Lee) Quantum K-invariants and Gopakumar-Vafa invariants I. The quintic threefold, arXiv:2211.00788
(Y.-C. Chou and Y.-P. Lee) Quantum K-invariants and Gopakumar-Vafa invariants II. Calabi-Yau threefolds at genus zero, arXiv:2305.08480
(Y.-C. Chou and Y.-P. Lee) Gopakumar-Vafa Invariants = Quantum K-invariants on Calabi-Yau threefolds, arXiv:2212.13432