Gromov Witten Theory Mirror Symmetry Birational Geometry and the Classificati...
Gromov Witten Theory Mirror Symmetry Birational Geometry and the Classification of Fano Manifolds
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...
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Información proyecto GWT
Duración del proyecto: 75 meses
Fecha Inicio: 2016-06-09
Fecha Fin: 2022-09-30
Fecha límite de participación
Sin fecha límite de participación.
Descripción del proyecto
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.