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Gromov-Witten Theory: Mirror Symmetry, Birational Geometry, and the Classification of Fano Manifolds (GWT)
Start date: Oct 1, 2016, End date: Sep 30, 2021 PROJECT  FINISHED 

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.

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