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GWT SIGNED

Gromov-Witten Theory: Mirror Symmetry, Birational Geometry, and the Classification of Fano Manifolds

Total Cost €

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EC-Contrib. €

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Partnership

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Project "GWT" data sheet

The following table provides information about the project.

Coordinator
IMPERIAL COLLEGE OF SCIENCE TECHNOLOGY AND MEDICINE 

Organization address
address: SOUTH KENSINGTON CAMPUS EXHIBITION ROAD
city: LONDON
postcode: SW7 2AZ
website: http://www.imperial.ac.uk/

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
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 Coordinator Country United Kingdom [UK]
 Project website http://coates.ma.ic.ac.uk
 Total cost 1˙999˙995 €
 EC max contribution 1˙999˙995 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2015-CoG
 Funding Scheme ERC-COG
 Starting year 2016
 Duration (year-month-day) from 2016-10-01   to  2021-09-30

 Partnership

Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    IMPERIAL COLLEGE OF SCIENCE TECHNOLOGY AND MEDICINE UK (LONDON) coordinator 1˙999˙995.00

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 Project objective

The classification of Fano manifolds is a long-standing and important open problem. Fano manifolds are basic building blocks in geometry: they are `atomic pieces' of mathematical shapes. We will take a radically new approach to Fano classification, combining Mirror Symmetry (a circle of ideas which originated in string theory) with new methods in geometry and massively-parallel computational algebra.

Our main geometric tool will be Gromov-Witten invariants. The Gromov-Witten invariants of a space X record the number of curves in X of a given genus and degree which meet a given collection of cycles in X; they have important applications in algebraic geometry, symplectic topology, and theoretical physics. We will develop powerful new methods for computing Gromov-Witten invariants, and will apply these methods to Fano classification and to questions in birational geometry.

 Publications

year authors and title journal last update
List of publications.
2017 Brini, Andrea
$E_8$ spectral curves
published pages: , ISSN: , DOI:
https://hal.archives-ouvertes.fr/hal-01639748 1 2019-09-09
2018 Argüz, Hülya; Prince, Thomas
On Real Lagrangians in Quintic Threefolds
published pages: , ISSN: , DOI:
1 2019-09-09
2017 Cavey, Daniel; Prince, Thomas
Del Pezzo surfaces with a single 1/k(1,1) singularity
published pages: , ISSN: , DOI:
3 2019-09-09
2018 Prince, Thomas
Lagrangian torus fibration models of Fano threefolds
published pages: , ISSN: , DOI:
1 2019-09-09
2018 Petracci, Andrea
Some examples of non-smoothable Gorenstein Fano toric threefolds
published pages: , ISSN: , DOI:
1 2019-09-09
2018 Coates, Tom; Manolache, Cristina
A splitting of the virtual class for genus one stable maps
published pages: , ISSN: , DOI:
1 2019-09-09
2019 Brini, Andrea
Exterior powers of the adjoint representation and the Weyl ring of $E_8$
published pages: , ISSN: , DOI:
1 2019-09-09
2018 Petracci, Andrea
Homogeneous deformations of toric pairs
published pages: , ISSN: , DOI:
2 2019-09-09
2019 T Coates, A Kasprzyk, T Prince
Laurent Inversion
published pages: , ISSN: 1558-8599, DOI:
Journal of Pure and Applied Mathematics Quarterly 2019-08-30
2019 E Kalashnikov, with an Appendix by T Coates, A Kasprzyk, and E Kalashnikov
Four dimensional Fano quiver flag zero loci
published pages: , ISSN: 1364-5021, DOI:
Proceedings of the Royal Society A 2019-08-30
2019 T Coates, H Iritani
Gromov-Witten Invariants of Local P^2 and Modular Forms
published pages: , ISSN: 2156-2261, DOI:
Kyoto Journal of Mathematics 2019-08-30

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