Objectif
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.
Champ scientifique
- natural sciencesmathematicspure mathematicstopologysymplectic topology
- natural sciencescomputer and information sciencescomputational science
- natural sciencesphysical sciencestheoretical physicsstring theory
- natural sciencesmathematicspure mathematicsgeometry
- natural sciencesmathematicspure mathematicsalgebraalgebraic geometry
Mots‑clés
Programme(s)
Régime de financement
ERC-COG - Consolidator GrantInstitution d’accueil
SW7 2AZ LONDON
Royaume-Uni