Objective
Bordism theory connects many central areas of mathematics: Defined via smooth manifolds, it has proved to have deep connections to formal groups from algebraic geometry and stable homotopy theory from algebraic topology. In particular, complex bordism serves as an effective organizational tool for studying the stable homotopy category, splitting up the homotopy groups of spheres into components of different wavelengths.
The goal of BorSym is to develop a similarly powerful correspondence that classifies the symmetry of spaces through novel connections to equivariant algebraic geometry and smooth actions. While such a relationship for symmetries has long been conjectured, it was only recently that foundational results have been established for the actions of abelian groups, such as the tensor-triangular classification of actions on finite complexes and my proof of the equivariant Quillen theorem. At the same time, bordism of symmetries has become a central object of interest also in the seemingly unrelated field of symplectic topology, where groundbreaking work of Abouzaid and collaborators has identified derived orbifold bordism as the universal target for Floer homology, thereby solving long-standing open problems in the field.
In view of these events a new picture is emerging which paints a universal role of equivariant bordism, going substantially beyond even its classical role described above. The goal of BorSym is to unravel the full potential of this emerging picture: to thoroughly develop a chromatic homotopy theory of group actions; to employ the newly established set of tools to tackle major open problems in transformation groups and obtain new information about the derived orbifold bordism ring; and to extend the connections between formal groups, thick subcategories and bordism rings beyond the abelian case.
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
- natural sciences mathematics pure mathematics 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)
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Multi-annual funding programmes that define the EU’s priorities for research and innovation.
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HORIZON.1.1 - 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.
HORIZON-ERC - HORIZON ERC Grants
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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-2024-STG
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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.
53113 Bonn
Germany
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.