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 (EuroSciVoc)
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
- natural sciences mathematics pure mathematics topology symplectic topology
- natural sciences physical sciences theoretical physics string theory
- natural sciences mathematics pure mathematics geometry
- natural sciences mathematics pure mathematics algebra algebraic geometry
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Keywords
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Programme(s)
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Topic(s)
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Call for proposal
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
ERC-2009-StG
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Funding Scheme
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Host institution
SW7 2AZ London
United Kingdom
The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.