Objective
Outstanding problems in a variety of mathematical fields have been shown to reduce, in essence, to questions about the combinatorial structure of the transfinite; this was the case, for example, in Shelah's solution to the Whitehead Problem in group theory, Farah's solution to the Brown-Douglas-Fillmore Problem in operator algebras, Solovay and Woodin's solution to Kaplansky's Conjecture on the automatic continuity of Banach algebras, and Moore's solution to the $L$ Space Problem in general topology. At the same time, cardinality and transfinite closing-off arguments play a critical role in many of the most fundamental constructions of contemporary category theory --- in the small object argument, the themes of local presentability and accessibility, or the invocation of Grothendieck universes, for example. Considerations of this latter sort play an insistent role in the 50-year-old problem of the existence of cohomological localizations in the categories of simplicial sets or spectra, a question which the work of this application's sponsor (among others at the University of Barcelona) suggests may well turn out, much as above, to be set theoretic in essence. Work on this problem forms the core of the present proposal, both for its instrinsic interest and bearing on multiple related conjectures (Hovey's Conjecture on Bousfield classes, most prominently), and for its relation, via the phenomenon of $\kappa$-phantom maps, to the researcher's accumulating results on the higher derived limits of large inverse systems. In its course, a number of related questions, for example on the cohomology of small cardinals, will receive close attention as well. This is, in short, a proposal to bring researchers from the divergent fields of algebraic topology and set theory together for work on a well-known problem which they may be uniquely well-suited to solve, and in the process to considerably extend the lines of research for which they are already known.
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 discrete mathematics mathematical logic
- natural sciences mathematics pure mathematics algebra
- natural sciences mathematics pure mathematics topology algebraic topology
- natural sciences mathematics pure mathematics mathematical analysis functional analysis operator algebra
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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.
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HORIZON.1.2 - Marie Skłodowska-Curie Actions (MSCA)
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-TMA-MSCA-PF-EF - HORIZON TMA MSCA Postdoctoral Fellowships - European Fellowships
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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) HORIZON-MSCA-2022-PF-01
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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.
08007 Barcelona
Spain
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.