Project description
Research throws more light on the computational and descriptive complexity of mathematical objects
Computable structure theory quantifies and studies the complexity of mathematical structures. The most common way to study their complexity is through degree spectra. Funded by the Marie Skłodowska-Curie Actions programme, the ACOSE project aims to further our understanding of the computational and descriptive complexity of mathematical objects (such as structures and relations) and their associated classification problems. Researchers will provide further insight into the overlooked relationship between the descriptive complexity of a set and the degree spectrum under a given equivalence relation. The newly developed techniques could help closely tie the fields of descriptive set theory and computable structure theory.
Objective
We will investigate the algorithmic complexity of mathematical structures and its connection with notions of complexity studied in descriptive set theory at. The main subject area of the planned research is computable structure theory — an area of logic concerning itself with the computational complexity of countable mathematical structures. Mathematicians usually consider structures up to some equivalence relation. For example, a number theorists works in the standard model of arithmetic, the natural numbers with addition and multiplication, but it is of little interest to him whether he works in the canonic representation or in some isomorphic copy as this does not impact his work.
However, for computational matters the choice of representation is highly important. Therefore one usually measures the algorithmic complexity of a structure by its degree spectrum, the set of Turing degrees of structure equivalent to the structure under a given equivalence relation.
Degree spectra are the main subject of investigation in computable structure theory. A natural way to think of degree spectra is as sets of subsets of the natural numbers, and these sets are studied in descriptive set theory.
So far the relation between the descriptive complexity of a set and whether it can be a degree spectrum under a given equivalence relation has been overlooked. The goal of this project is to relate the descriptive complexity of sets with their realizability as degree spectra under some equivalence relation.
We plan to obtain new results and develop new techniques which will be beneficial to both descriptive set theory and computable structure theory and hope to form a lasting connection between those fields.
The fellowship will be carried out over 36 months, 24 months at the University of California, Berkeley under supervision of Prof. Antonio Montalbán and 12 months at TU Wien under the supervision of Professors Ekaterina Fokina and Matthias Baaz.
Fields of science (EuroSciVoc)
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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.
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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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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-2020
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1040 Wien
Austria
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