Computer Science: Swansea University Research Excellence Scholarship (SURES): Fully Funded PhD Scholarship: Enumeration degrees and topology

Funding provider: Swansea University

Subject areas: Computer Science / Mathematics

Project start date:

• 1 October 2024 (Enrolment open from mid-September)

Supervisor: Dr Arno Pauly ([email protected])

Aligned programme of study: PhD in Computer Science

Mode of study: Full-time

Project description: 

Research at the Faculty of Science and Engineering

Kihara and Pauly recently uncovered an intricate connection between computability theory and topology (“Point degree spectra of represented spaces”, Forum of Mathematics Sigma 2022). 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 (i.e. a student who is eligible to pay the UK rate of tuition fees) 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. 

• Where applicants have multiple master’s degrees, a distinction must be held in the degree that is most relevant to the intended PhD study. 
• If you are currently studying for a master’s level qualification with an expected award date that is later than 01/10/2024, you should hold a minimum of an upper-second-class (2:1) honours degree.   
• You should be able to demonstrate a pass with a minimum grade average of at least 70% for your part-one master’s degree modules (the taught aspect of your master’s course rather than a research-focused dissertation) and submit your dissertation by no later than 30/09/2024.  

Applicants must be able to begin their course of study in October 2024. As a cohort-based programme, deferral to an alternative enrolment window within the academic year or to another academic year is not permissible.

Please note that both the degree and language-proficiency entry requirements for SURES are higher than the baseline standard for entry that is stipulated for most of the PhD programmes at Swansea University. 

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.