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

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.

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Coordinator

IMPERIAL COLLEGE OF SCIENCE TECHNOLOGY AND MEDICINE
Net EU contribution
€ 1 999 995,00
Address
South kensington campus exhibition road
SW7 2AZ London
United Kingdom

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Region
London Inner London — West Westminster
Activity type
Higher or Secondary Education Establishments
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Other funding
€ 0,00

Beneficiaries (1)