Objective
This proposal is concerned with the homological properties of Calabi-Yau threefolds, the geometric structures which play a crucial role in string theory. Rather than working directly with categories of sheaves, we focus on a closely-related class of models defined using quivers with potentials, which have themselves been the subject of intensive research over the last decade.
Associated to a quiver with potential are two complex manifolds: the space of stability conditions and the cluster variety. Recent work by physicists Gaiotto, Moore and Neitzke suggests that there is a remarkable geometric relationship between these spaces, involving Donaldson-Thomas invariants and the Kontsevich-Soibelman wall-crossing formula. Work by the PI and others over the last couple of years has paved the way for a rigorous mathematical understanding of this relationship. This has the potential to open up new vistas in algebra and geometry, as well as greatly enhancing our understanding of the mathematics of quantum field theory.
Our proposal combines powerful general constructions with specific computable examples. We will work initially with a class of examples related to triangulated surfaces; here the relevant spaces can be identified with familiar objects in the topology of surfaces, including moduli spaces of quadratic differentials, projective structures and local systems. These examples already involve deep mathematics, and are closely related to quantum field theories of current interest in theoretical physics.
This proposal involves an unusually wide range of mathematics. Our ambition is to assemble a team of 4 research assistants having a sufficiently broad expertise to make progress on this exciting multi-disciplinary project. The PI is in a perfect position to lead such a team: he invented stability conditions, carried out important work on Donaldson-Thomas invariants, and proved a major theorem which forms one of the starting points of the proposal.
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
- natural sciences physical sciences quantum physics quantum field theory
- natural sciences mathematics pure mathematics algebra
- natural sciences physical sciences theoretical physics string theory
- natural sciences mathematics pure mathematics geometry
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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.
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H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC)
MAIN PROGRAMME
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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.
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.
ERC-ADG - Advanced Grant
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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.
(opens in new window) ERC-2014-ADG
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Net EU financial contribution. The sum of money that the participant receives, deducted by the EU contribution to its linked third party. It considers the distribution of the EU financial contribution between direct beneficiaries of the project and other types of participants, like third-party participants.
S10 2TN SHEFFIELD
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.