---
_id: '10772'
abstract:
- lang: eng
  text: We introduce tropical corals, balanced trees in a half-space, and show that
    they correspond to holomorphic polygons capturing the product rule in Lagrangian
    Floer theory for the elliptic curve. We then prove a correspondence theorem equating
    counts of tropical corals to punctured log Gromov–Witten invariants of the Tate
    curve. This implies that the homogeneous coordinate ring of the mirror to the
    Tate curve is isomorphic to the degree-zero part of symplectic cohomology, confirming
    a prediction of homological mirror symmetry.
acknowledgement: 'This paper is based on my PhD thesis, which would not be possible
  without the support of my advisor Bernd Siebert. I also thank Dan Abramovich, Mohammed
  Abouzaid, Mark Gross, Tom Coates and Dimitri Zvonkine for many useful conversations.
  Finally, I thank the anonymous referees for their many insightful comments and valuable
  suggestions which have resulted in major improvements to this article. This project
  has received funding from the EuropeanResearch Council (ERC) under the European
  Union’s Horizon 2020 research and innovation programme (Grant Agreement Number:
  682603), and from Fondation Mathématique Jacques Hadamard. '
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Nuroemuer Huelya
  full_name: Arguez, Nuroemuer Huelya
  id: 3c26b22e-c843-11eb-aa56-d38ffa0bdd08
  last_name: Arguez
citation:
  ama: Arguez NH. Mirror symmetry for the Tate curve via tropical and log corals.
    <i>Journal of the London Mathematical Society</i>. 2022;105(1):343-411. doi:<a
    href="https://doi.org/10.1112/jlms.12515">10.1112/jlms.12515</a>
  apa: Arguez, N. H. (2022). Mirror symmetry for the Tate curve via tropical and log
    corals. <i>Journal of the London Mathematical Society</i>. London Mathematical
    Society. <a href="https://doi.org/10.1112/jlms.12515">https://doi.org/10.1112/jlms.12515</a>
  chicago: Arguez, Nuroemuer Huelya. “Mirror Symmetry for the Tate Curve via Tropical
    and Log Corals.” <i>Journal of the London Mathematical Society</i>. London Mathematical
    Society, 2022. <a href="https://doi.org/10.1112/jlms.12515">https://doi.org/10.1112/jlms.12515</a>.
  ieee: N. H. Arguez, “Mirror symmetry for the Tate curve via tropical and log corals,”
    <i>Journal of the London Mathematical Society</i>, vol. 105, no. 1. London Mathematical
    Society, pp. 343–411, 2022.
  ista: Arguez NH. 2022. Mirror symmetry for the Tate curve via tropical and log corals.
    Journal of the London Mathematical Society. 105(1), 343–411.
  mla: Arguez, Nuroemuer Huelya. “Mirror Symmetry for the Tate Curve via Tropical
    and Log Corals.” <i>Journal of the London Mathematical Society</i>, vol. 105,
    no. 1, London Mathematical Society, 2022, pp. 343–411, doi:<a href="https://doi.org/10.1112/jlms.12515">10.1112/jlms.12515</a>.
  short: N.H. Arguez, Journal of the London Mathematical Society 105 (2022) 343–411.
date_created: 2022-02-20T23:01:33Z
date_published: 2022-02-05T00:00:00Z
date_updated: 2023-08-02T14:29:50Z
day: '05'
ddc:
- '510'
department:
- _id: TaHa
doi: 10.1112/jlms.12515
external_id:
  arxiv:
  - '1712.10260'
  isi:
  - '000751600600001'
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  date_created: 2022-02-21T11:22:58Z
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has_accepted_license: '1'
intvolume: '       105'
isi: 1
issue: '1'
language:
- iso: eng
month: '02'
oa: 1
oa_version: Published Version
page: 343-411
publication: Journal of the London Mathematical Society
publication_identifier:
  eissn:
  - 1469-7750
  issn:
  - 0024-6107
publication_status: published
publisher: London Mathematical Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: Mirror symmetry for the Tate curve via tropical and log corals
tmp:
  image: /images/cc_by_nc_nd.png
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...