Objective
"Over the last decade, homological algebra has entered symplectic topology, largely thanks to the appearance of Fukaya categories in homological mirror symmetry. Applications of these new methods and ideas are still scarce. We propose a fundamentally new approach to studying symplectic dynamics, by studying the action of the symplectic mapping class group on the complex manifold of stability conditions on its Fukaya category. This can be seen as a first attempt to generalise classical Teichmueller theory to higher-dimensional symplectic manifolds. Many invariants arising in low-dimensional topology, including Khovanov cohomology for knots, are governed by the Fukaya categories of associated moduli spaces. We propose an ""uncertainty principle"" in topology, in which these invariants are intrinsically constrained by rigidity of this underlying categorical structure. Besides applications in topology, this suggests a framework for studying the sense in which topological complexity is the shadow of dynamical complexity."
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 mathematics pure mathematics algebra
- natural sciences mathematics pure mathematics topology algebraic topology
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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-2007-StG
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.
Host institution
CB2 1TN CAMBRIDGE
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.