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Research Excellence Scholarship

3 months ago

Swansea, City and County of Swansea, United Kingdom Swansea University Full time

Funding providers: Swansea University

Subject areas: Computer Science / Mathematics

Project start date: 1 October 2024 (Enrolment open from mid-September)

Project description:

Kihara and Pauly recently uncovered an intricate connection between computability theory and topology ("Point degree spectra of represented spaces", Forum of Mathematics Sigma They associate a degree structure (called degree spectrum) to a topological space which reflects many of its topological characteristics. For example, the real numbers are associated with the Turing degrees. This connection already has been used to obtain new results in topology using computability-theoretic methods and vice versa, including solving a long-open question by Jayne on the number of sigma-homeomorphism types of Polish spaces. This project is about further exploring this connection.

Concrete research objectives include calculating the degree spectra of more topological spaces exhibiting unusual properties, and to identify topological properties linked to classes of degrees such as the uniformly intro-enumerable ones. A big open question in this area is whether every almost-total enumeration degree is graph-cototal.

Background knowledge in some of pointset topology, computability theory, dimension theory or logic would be helpful.

Eligibility

Candidates must have attained, or must be expected to attain, a first-class honours degree and/or a distinction at master's level. If you are eligible to apply for the scholarship but do not hold a UK degree, you can check our comparison entry requirements. Please note that you may need to provide evidence of your English Language proficiency.

Due to funding restrictions, this scholarship is open to applicants eligible to pay tuition fees at the UK rate only, as defined by UKCISA regulations.

Additional Funding Information

This scholarship covers the full cost of UK tuition fees and an annual stipend at UKRI rate (currently £18,622 for 2023/24).

Additional research expenses will also be available.

£19,237 p.a.