Objective
Calabi-Yau 3-folds are 6-dimensional spaces with a rich geometrical structure. In Mathematics, Calabi-Yau 3-folds are interesting to Algebraic, Symplectic and Differential Geometers. In Physics, they are essential ingredients for building a universe: String Theory claims the universe has 10 dimensions, and is the product of a large 4-dimensional space-time with a small Calabi-Yau 3-fold. String Theorists made some strange and exciting conjectures about Calabi-Yau 3-folds, known as "Mirror Symmetry". Many of these concern "invariants", numbers associated to the Calabi-Yau 3-fold, which for deep reasons depend on only part of the geometric structure. This proposal concerns "Donaldson-Thomas (D-T) invariants" of Calabi-Yau 3-folds M. These are integers which "count" geometric objects called coherent sheaves on M. The definition of D-T invariants uses algebraic geometry, and requires both a symplectic structure (polarization) and a complex structure, but the invariants are unchanged by deformations of the complex structure. Our goal is to find a new symplectic definition of D-T invariants using gauge theory. Given a compact symplectic 6-manifold with c1=0 we choose a compatible generic almost complex structure J and define new "analytic D-T invariants" which "count" solutions of a gauge-theory equation generalizing Hermitian-Einstein connections. This is a substitute for counting holomorphic vector bundles, the simplest kind of coherent sheaf. The difficult issues concern compactness of the moduli spaces, and understanding limits of solutions. We aim to show these analytic D-T invariants are independent of J, and depend only on M as a symplectic manifold. We aim to formulate a "generalized MNOP conjecture" which expresses usual D-T invariants in terms of our analytic D-T invariants and the Gromov-Witten invariants and Betti numbers of M. This brings D-T invariants into symplectic geometry, and also reveals new symmetries and structure in D-T invariants.
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: https://op.europa.eu/en/web/eu-vocabularies/euroscivoc.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: https://op.europa.eu/en/web/eu-vocabularies/euroscivoc.
- 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
You need to log in or register to use this function
We are sorry... an unexpected error occurred during execution.
You need to be authenticated. Your session might have expired.
Thank you for your feedback. You will soon receive an email to confirm the submission. If you have selected to be notified about the reporting status, you will also be contacted when the reporting status will change.
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.
FP7-PEOPLE-IIF-2008
See other projects for this call
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.
Coordinator
OX1 2JD Oxford
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.