Objective
Group theory is the study of symmetry in mathematical objects, such as rotations of geometric shapes.
Groups help us understand the underlying structure of mathematical objects by revealing their symmetries.
To understand groups we need an efficient way to describe them. Some groups admit a finite presentation;
a finite set of building blocks, along with a finite collection of rules on when we can substitute one set
of blocks for another. These descriptions are convenient. However, results in algebra and logic show
that such descriptions are not always suitable to work with, as certain problems (e.g. the word problem,
of deciding if two distinct collections of blocks represent the same group element) are incomputable; no
computer can be built to always answer this. We can embed incomputable problems from groups into
geometry, to show that the homeomorphism problem, of recognising if two geometric shapes are equivalent
under smooth deformation, is incomputable in all dimensions above three. Thus we can't computationally
classify geometric shapes in higher dimensions; we can't identify the unique distinguishing features of
each shape. The study of generic computability (problems which can be computed most of the time) is
a useful area in mathematics. Conversely, showing a problem can't be computed most of the time gives
rise to applications in cryptography: generically incomputable problems are an excellent tool in the theory
behind cryptosystems. This proposal will deal with incomputable and generically incomputable problems.
We will investigate certain problems in group theory to determine if they are computable, or generically
computable, or neither. We will apply these results to particular classess of higher-dimensional geometric
objects, identifying whether certain problems relating to them are computable or not. The project will be
carried out at the University of Cambridge, under the supervision of Dr. Henry Wilton.
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 computer and information sciences internet
- natural sciences mathematics pure mathematics topology
- natural sciences computer and information sciences computer security cryptography
- natural sciences mathematics pure mathematics algebra
- 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-EF-ST - Standard EF
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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-2014
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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.
CB2 1TN CAMBRIDGE
United Kingdom
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.