Homological mirror symmetry, Hodge theory, and symplectic topology

Project Information

HMS

Grant agreement ID: 850713

DOI

10.3030/850713

Project closed

EC signature date 20 September 2019

Start date 1 March 2020

End date 31 August 2025

Funded under

• EXCELLENT SCIENCE - European Research Council (ERC)

Total cost

€ 1 498 686,00

EU contribution

€ 1 498 686,00

Coordinated by

THE UNIVERSITY OF EDINBURGH
United Kingdom

CORDIS provides links to public deliverables and publications of HORIZON projects.

Links to deliverables and publications from FP7 projects, as well as links to some specific result types such as dataset and software, are dynamically retrieved from OpenAIRE .

Publications

Other (23)

Equivariant Floer homotopy via Morse-Bott theory

Author(s): Côté, Laurent; Kartal, Yusuf Barış
Published in: arxiv preprint, 2023
Publisher: NA
DOI: 10.48550/arxiv.2309.15089

The cyclic open--closed map and variations of Hodge structures

Author(s): Sheel Ganatra, Nick Sheridan
Published in: 2025
Publisher: arXiv preprint

An open GW-formula for Lagrangians in Fano varieties

Author(s): Alami, Mohamed El
Published in: arxiv preprint, 2023
Publisher: NA
DOI: 10.48550/arxiv.2305.02102

An L-infinity structure on symplectic cohomology

Author(s): Matthew Strom Borman, Mohamed El Alami, Nick Sheridan
Published in: arxiv preprint, 2024
Publisher: NA

Lagrangian cobordisms and K-theory of symplectic bielliptic surfaces

Author(s): Alvaro Muniz-Brea
Published in: arxiv preprint, 2024
Publisher: NA

Dimensionality of tropical Chow groups

Author(s): Alvaro Muniz Brea
Published in: arxiv preprint, 2024
Publisher: NA

Recovering generalized homology from Floer homology: the complex oriented case

Author(s): Laurent Cote, Yusuf Baris Kartal
Published in: arxiv preprint, 2024
Publisher: NA

Symplectic $\mathbb{C}^*$-manifolds II: Morse-Bott-Floer Spectral Sequences

Author(s): Ritter, Alexander F.; Živanović, Filip
Published in: Arxiv preprint, 2023
Publisher: NA
DOI: 10.48550/arxiv.2304.14384

On the mirrors of low-degree del Pezzo surfaces

Author(s): Giulia Gugiatti, Franco Rota
Published in: 2025
Publisher: arXiv preprint

Mirror symmetry: from categories to curve counts

Author(s): Sheel Ganatra, Timothy Perutz, Nick Sheridan
Published in: arXiv preprint, 2025
Publisher: arXiv preprint

Symplectic $\mathbb{C}^*$-manifolds I: Filtration on Quantum Cohomology

Author(s): Ritter, Alexander F.; Živanović, Filip
Published in: Arxiv preprint, 2023
Publisher: NA
DOI: 10.48550/arxiv.2304.13026

Fourier transforms and a filtration on the Lagrangian cobordism group of tori

Author(s): Álvaro Muñiz Brea
Published in: 2024
Publisher: Arxiv preprint

Homological mirror symmetry for Batyrev mirror pairs

Author(s): Sheel Ganatra, Andrew Hanlon, Jeffrey Hicks, Daniel Pomerleano, Nick Sheridan
Published in: arxiv preprint, 2024
Publisher: NA

Lagrangian skeleta of very affine complete intersections

Author(s): Danil Koževnikov
Published in: arXiv preprint, 2025
Publisher: arXiv preprint

Iterations of symplectomorphisms and p-adic analytic actions on Fukaya category

Author(s): Yusuf Baris Kartal
Published in: 2024
Publisher: NA

Exact Lagrangians from contracting C*-actions

Author(s): Filip Zivanovic
Published in: arXiv preprint, 2022
Publisher: NA

Examples of relative quantum cohomology

Author(s): Hugtenburg, Kai; Tukachinsky, Sara B.
Published in: arxiv preprint, 2024
Publisher: NA
DOI: 10.48550/arxiv.2402.03209

On the quantum differential equations for a family of non-Kähler monotone symplectic manifolds

Author(s): Hugtenburg, Kai
Published in: arxiv preprint, 2024
Publisher: NA
DOI: 10.48550/arxiv.2402.10867

Symplectic higher Auslander correspondence for type A

Author(s): Ilaria Di Dedda
Published in: arxiv preprint, 2024
Publisher: arxiv preprint

On the positivity and integrality of coefficients of mirror maps

Author(s): Sophie Bleau, Nick Sheridan
Published in: arxiv preprint, 2024
Publisher: NA

Maurer-Cartan elements in symplectic cohomology from compactifications

Author(s): Matthew Strom Borman, Mohamed El Alami, Nick Sheridan
Published in: arxiv preprint, 2024
Publisher: NA

Constructing the big relative Fukaya category, and its open--closed maps

Author(s): Nick Sheridan
Published in: arXiv preprint, 2025
Publisher: arXiv preprint

Some cute applications of Lagrangian cobordisms towards examplesin quantitative symplectic geometry

Author(s): Jeff Hicks, Cheuk Yu Mak
Published in: arXiv preprint, 2022
Publisher: NA

Peer reviewed articles (12)

Constructing the relative Fukaya category

Author(s): Timothy Perutz, Nick Sheridan
Published in: Journal of Symplectic Geometry, 2023, ISSN 1527-5256
Publisher: International Press

Open Gromov-Witten invariants from the Fukaya category

Author(s): Kai Hugtenburg
Published in: Advances in Mathematics, Issue 441, 2024, Page(s) 109542, ISSN 0001-8708
Publisher: Academic Press
DOI: 10.1016/j.aim.2024.109542

Quantum cohomology as a deformation of symplectic cohomology

Author(s): Matthew Strom Borman, Nick Sheridan, Umut Varolgunes
Published in: J. Fixed Point Theory Appl., Issue 16617738, 2022, ISSN 1661-7738
Publisher: Birkhäuser Verlag
DOI: 10.1007/s11784-022-00965-6

The cyclic open–closed map, u-connections and R-matrices

Author(s): Kai Hugtenburg
Published in: Selecta Mathematica, Issue 30, 2024, ISSN 1022-1824
Publisher: Birkhauser Verlag
DOI: 10.1007/s00029-024-00925-7

Integrality of mirror maps and arithmetic homological mirror symmetry for Greene–Plesser mirrors

Author(s): Sheel Ganatra, Andrew Hanlon, Jeff Hicks, Daniel Pomerleano, Nick Sheridan
Published in: Advances in Mathematics, Issue 481, 2025, Page(s) 110535, ISSN 0001-8708
Publisher: Academic Press
DOI: 10.1016/j.aim.2025.110535

Wall-crossing from Lagrangian cobordisms

Author(s): Jeff Hicks
Published in: Algebraic & Geometric Topology, Issue 24, 2024, Page(s) 3069-3138, ISSN 1472-2747
Publisher: Geometry & Topology Publications
DOI: 10.2140/agt.2024.24.3069

Locality of relative symplectic cohomology for complete embeddings

Author(s): Yoel Groman, Umut Varolgunes
Published in: Compositio Mathematica, Issue 159, 2023, Page(s) 2551-2637, ISSN 0010-437X
Publisher: London Mathematical Society
DOI: 10.1112/s0010437x23007492

Iterations of symplectomorphisms and $p$-adic analytic actions on the Fukaya category

Author(s): Yusuf Barış Kartal
Published in: Inventiones mathematicae, Issue 239, 2025, Page(s) 801-864, ISSN 0020-9910
Publisher: Springer Verlag
DOI: 10.1007/s00222-024-01308-7

Automatic split-generation for the Fukaya category

Author(s): Timothy Perutz, Nick Sheridan
Published in: International Mathematics Research Notices, 2023, ISSN 1073-7928
Publisher: Oxford University Press
DOI: 10.1093/imrn/rnac363

Lagrangian cobordisms and Lagrangian surgery

Author(s): Jeff Hicks
Published in: Commentarii Mathematici Helvetici, Issue 98, 2024, Page(s) 509-595, ISSN 0010-2571
Publisher: Birkhauser Verlag
DOI: 10.4171/cmh/554

Realizability in tropical geometry and unobstructedness of Lagrangian submanifolds

Author(s): Jeffrey Hicks
Published in: Geometry & Topology, Issue 29, 2025, Page(s) 1909-1973, ISSN 1465-3060
Publisher: University of Warwick
DOI: 10.2140/gt.2025.29.1909

Resolutions of toric subvarieties by line bundles and applications

Author(s): Andrew Hanlon, Jeff Hicks, Oleg Lazarev
Published in: Forum of Mathematics, Pi, Issue 12, 2024, ISSN 2050-5086
Publisher: Cambridge University Press (CUP)
DOI: 10.1017/fmp.2024.21