Objective 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 geometry, and theoretical physics. The program proposed here will allow us to compute Gromov-Witten invariants, and particularly higher-genus Gromov-Witten invariants, for a very broad class of spaces. Recent progress, partly due to the Principal Investigator, has led to a greatly-improved mathematical understanding of the string-theoretic duality known as Mirror Symmetry. This allows us to compute genus-zero Gromov-Witten invariants (those where the curves involved are spheres) for a wide range of target spaces. But at the moment there are very few effective tools for computing higher-genus Gromov-Witten invariants (those where the curves involved are tori, or n-holed tori for n>1). We will solve this problem by extending mathematical Mirror Symmetry to cover this case. In doing so we will draw on and make rigorous recent insights from topological string theory. These insights have revealed close and surprising connections between Gromov-Witten theory, modular forms, and the theory of integrable systems. Fields of science natural sciencesmathematicspure mathematicstopologysymplectic topologynatural sciencesphysical sciencestheoretical physicsstring theorynatural sciencesmathematicspure mathematicsgeometrynatural sciencesmathematicspure mathematicsalgebraalgebraic geometry Keywords algebraic geometry mirror symmetry symplectic geometry topological string theory Programme(s) FP7-IDEAS-ERC - Specific programme: "Ideas" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013) Topic(s) ERC-SG-PE1 - ERC Starting Grant - Mathematical foundations Call for proposal ERC-2009-StG See other projects for this call Funding Scheme ERC-SG - ERC Starting Grant Host institution IMPERIAL COLLEGE OF SCIENCE TECHNOLOGY AND MEDICINE EU contribution € 620 000,00 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 Administrative Contact Brooke Alasya (Ms.) Principal investigator Tom Coates (Dr.) Links Contact the organisation Opens in new window Website Opens in new window Total cost No data Beneficiaries (1) Sort alphabetically Sort by EU Contribution Expand all Collapse all IMPERIAL COLLEGE OF SCIENCE TECHNOLOGY AND MEDICINE United Kingdom EU contribution € 620 000,00 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 Administrative Contact Brooke Alasya (Ms.) Principal investigator Tom Coates (Dr.) Links Contact the organisation Opens in new window Website Opens in new window Total cost No data
