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. Fields of science natural sciencesmathematicspure mathematicstopologysymplectic topologynatural sciencescomputer and information sciencescomputational sciencenatural sciencesphysical sciencestheoretical physicsstring theorynatural sciencesmathematicspure mathematicsgeometrynatural sciencesmathematicspure mathematicsalgebraalgebraic geometry Keywords Mirror Symmetry Gromov-Witten Invariants Fano Manifolds Birational Geometry Computational Algebra Programme(s) H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC) Main Programme Topic(s) ERC-CoG-2015 - ERC Consolidator Grant Call for proposal ERC-2015-CoG See other projects for this call Funding Scheme ERC-COG - Consolidator Grant Host institution 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 See on map Region London Inner London — West Westminster Activity type Higher or Secondary Education Establishments Links Contact the organisation Opens in new window Website Opens in new window Participation in EU R&I programmes Opens in new window HORIZON collaboration network Opens in new window Total cost € 1 999 995,00 Beneficiaries (1) Sort alphabetically Sort by Net EU contribution Expand all Collapse all IMPERIAL COLLEGE OF SCIENCE TECHNOLOGY AND MEDICINE United Kingdom Net EU contribution € 1 999 995,00 Address SOUTH KENSINGTON CAMPUS EXHIBITION ROAD SW7 2AZ LONDON See on map Region London Inner London — West Westminster Activity type Higher or Secondary Education Establishments Links Contact the organisation Opens in new window Website Opens in new window Participation in EU R&I programmes Opens in new window HORIZON collaboration network Opens in new window Total cost € 1 999 995,00