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GWT SIGNED

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

Total Cost €

EC-Contrib. €

Partnership

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Outcomes and
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GWT project word cloud

Explore the words cloud of the GWT project. It provides you a very rough idea of what is the project "GWT" about.

witten building meet geometry symmetry theoretical radically circle genus geometric cycles curves collection blocks algebraic gromov mirror invariants ideas algebra computing manifolds record string topology massively parallel computational combining atomic powerful mathematical symplectic tool questions originated pieces birational classification shapes fano basic theory space degree physics

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. telephone: n.a. fax: n.a.
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 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. telephone: n.a. fax: n.a.	UK (LONDON)	coordinator	1˙999˙995.00

Map

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

List of publications.
year	authors and title	journal	last update
2017	Brini, Andrea $E_8$ spectral curves published pages: , ISSN: , DOI:	https://hal.archives-ouvertes.fr/hal-01639748 1	2019-09-09
2018	ArgÃ¼z, HÃ¼lya; 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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