Summary
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.
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.
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| Web resources: | https://cordis.europa.eu/project/id/682603 |
| Start date: | 01-10-2016 |
| End date: | 30-09-2022 |
| Total budget - Public funding: | 1 999 995,00 Euro - 1 999 995,00 Euro |
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Original description
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.
Status
CLOSEDCall topic
ERC-CoG-2015Update Date
27-04-2024
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