Project description
A universal topological field theory with values in graph complexes
Topology, historically a topic of mathematics, has gained critical practical value and significantly renewed interest with the discovery of topological materials and advances in accessing topological states of matter. The ERC-funded GRAPHCPX aims to create a universal topological field theory with values in graph complexes uniting areas of mathematical physics, topology, homological algebra, and algebraic geometry. It could provide: a precise topological interpretation of a class of well-studied topological field theories; new tools to study objects like configuration and embedding spaces and potentially diffeomorphism groups; and a wealth of new algebraic structures on graph complexes, some of the most important objects in the field.
Objective
The goal of the proposed project is to create a universal (AKSZ type) topological field theory with values in graph complexes, capturing the rational homotopy types of manifolds, configuration and embedding spaces.
If successful, such a theory will unite certain areas of mathematical physics, topology, homological algebra and algebraic geometry. More concretely, from the physical viewpoint it would give a precise topological interpretation of a class of well studied topological field theories, as opposed to the current state of the art, in which these theories are defined by giving formulae without guarantees on the non-triviality of the produced invariants.
From the topological viewpoint such a theory will provide new tools to study much sought after objects like configuration and embedding spaces, and tentatively also diffeomorphism groups, through small combinatorial models given by Feynman diagrams. In particular, this will unite and extend existing graphical models of configuration and embedding spaces due to Kontsevich, Lambrechts, Volic, Arone, Turchin and others.
From the homological algebra viewpoint a field theory as above provides a wealth of additional algebraic structures on the graph complexes, which are some of the most central and most mysterious objects in the field.
Such algebraic structures are expected to yield constraints on the graph cohomology, as well as ways to construct series of previously unknown classes.
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 applied mathematics mathematical physics
- natural sciences mathematics pure mathematics topology algebraic topology
- 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.
-
H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC)
MAIN PROGRAMME
See all projects funded under this programme
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-STG - Starting Grant
See all projects funded under this funding scheme
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-2015-STG
See all projects funded under this callHost institution
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.
8092 Zuerich
Switzerland
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.