Project description
Building a stronger connection between topological and algebraic K-theory
In mathematics, K-theory is the study of a ring generated by vector bundles over a topological space. In general, there are two main types of K-theory: topological and algebraic. The goal of the EU-funded K-theory project is to find strong connections between these two types. The project will extend prior work which established the foundations of a real algebraic K-theory spectrum that led to a solution of a conjecture of Hesselholt–Madsen. It will also take into account recent results in algebraic K-theory that prove the existence of a ring spectrum – the circle-dot ring – which determines the failure of excision in K-theory.
Objective
Algebraic $K$-theory -- Arithmetic and Topology. The goal of the proposed project is to use recent results in algebraic K-theory to further the connection between algebraic K-theory on the one hand, and arithmetic and topology on the other. This will split the proposed project into two parts: The one exhibiting connections to topology, more precisely the topology of manifolds and Poincaré duality spaces, and the other exhibiting connections to arithmetic geometry, more precisely gaining access at explicit calculations of K-theory groups of (spectral) schemes. Both main goals build on previous work in which I played a role, on the one hand establishing the foundations of a new ``real algebraic K-theory spectrum'' which leads in particular to a solution of a conjecture of Hesselholt--Madsen, and on the other hand a recent result in algebraic K-theory which proves the existence of a ring spectrum, the circle-dot ring, which determines the failure of excision in K-theory. The pure existence (and some formal properties) of this ring have already been exploited for many applications, and the goal of this part of the project is to make the circle-dot ring more explicit and use this new knowledge for explicit computations.
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 arithmetics
- 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.1.3. - EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions
MAIN PROGRAMME
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H2020-EU.1.3.2. - Nurturing excellence by means of cross-border and cross-sector mobility
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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.
MSCA-IF - Marie Skłodowska-Curie Individual Fellowships (IF)
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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) H2020-MSCA-IF-2019
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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.
1165 KOBENHAVN
Denmark
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.