Computer Science: Fully Funded EPSRC and Swansea University PhD Scholarship: Effective dimensions: applications of computability theory to geometric measure theory (RS459)

Funding providers: EPSRC and Swansea University's Faculty of Science and Engineering

Subject areas: Computability theory, computable analysis, geometric measure theory, effective descriptive set theory 

Project start date: 

• 1 October 2024 (Enrolment open from mid-September)
• 1 January 2025 (Enrolment open from mid-December)

Supervisors:

• Dr Manlio Valenti (manlio.valenti@swansea.ac.uk)
  Dr Arno Pauly

Aligned programme of study: PhD in Computer Science

Mode of study: Full-time 

Project description: 

Recent works showed how tools from computability theory and computable analysis can be used to study the geometric properties of sets. In particular, the Point-to-Set Principle provides an explicit connection between the Hausdorff dimension of a set (a notion of fundamental importance in analysis and geometric measure theory) and the Kolmogorov complexity of its points (a computability-theoretical notion that measures the “(in)compressibility” of a string). This resulted in a new wave of results, both in computability theory and in other areas of mathematics, and some theorems in geometric measure theory have been proven, for the first time, using these tools. 

The quest for point-to-set principles can be condensed into the question “If a set has a certain structural/topological property, what are the computability-theoretical characteristics of its points?”. The goal of this project is to strengthen the connection between computable analysis and “classical” mathematics, and exploring computability-theoretical notions affect the geometric structure of sets. 

This project is naturally connected with several topics in theoretical computer science and mathematics, including of course computability theory and geometric measure theory, but also (effective) descriptive set theory, harmonic analysis, and algorithmic information theory. The ideal candidate would have a strong background in mathematics, theoretical computer science, or related topics. Prior exposure to (some of) the above topics is preferred but not required.

Candidates must hold an undergraduate degree at 2.1 level in Computer Science, Mathematics or a closely related discipline, or an appropriate master’s degree with a minimum overall grade at ‘Merit’ (or Non-UK equivalent as defined by Swansea University). 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 (see country specific qualifications). Please note that you may need to provide evidence of your English Language proficiency. 

English Language: IELTS 6.5 Overall (with no individual component below 6.0) or Swansea University recognised equivalent. Full details of our English Language policy, including certificate time validity, can be found here.

This scholarship is open to candidates of any nationality.

EPSRC funded studentships are available to home and international students. Up to 30% of our cohort can comprise international students, once the limit has been reached, we are unable to make offers to international students.  

We are still accepting applications from international applicants.   

International students will not be charged the fee difference between the UK and international rate. Applicants should satisfy the UKRI eligibility requirements. 

ATAS

Please note that the programme requires some applicants to hold ATAS clearance, further details on ATAS scheme eligibility are available on the UK Government website. 

ATAS clearance IS NOT required to be held as part of the scholarship application process, successful award winners (as appropriate) are provided with details as to how to apply for ATAS clearance in tandem with scholarship course offer. 

If you have any questions regarding your academic or fee eligibility based on the above, please email pgrscholarships@swansea.ac.uk with the web-link to the scholarship(s) you are interested in. 

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

Additional research expenses will also be available.

To apply, please complete your application online with the following information:

1. Course choice – please select Computer Science / PhD / Full-time / 3 Year / October

   In the event you have already applied for the above programme previously, the application system may issue a warning notice and prevent application, in this event, please email pgrscholarships@swansea.ac.uk where staff will be happy to assist you in submitting your application.

2. Start year – please select 2024
3. Funding (page 8) –

• ‘Are you funding your studies yourself?’ – please select No
• ‘Name of Individual or organisation providing funds for study’ – please enter ‘RS459 - Measure Theory’

*It is the responsibility of the applicant to list the above information accurately when applying, please note that applications received without the above information listed will not be considered for the scholarship award.

One application is required per individual Swansea University led research scholarship award; applications cannot be considered listing multiple Swansea University led research scholarship awards.

We encourage you to complete the following to support our commitment to providing an environment free of discrimination and celebrating diversity at Swansea University: 

• Equality, Diversity and Inclusion (EDI) Monitoring Form (online form) 

As part of your online application, you MUST upload the following documents (please do not send these via email):

• CV
• Degree certificates and transcripts (if you are currently studying for a degree, screenshots of your grades to date are sufficient)
• A cover letter including a ‘Supplementary Personal Statement’ to explain why the position particularly matches your skills and experience and how you choose to develop the project.
• Two references (academic or previous employer) on headed paper or using the Swansea University reference form. Please note that we are not able to accept references received citing private email accounts, e.g. Hotmail. Referees should cite their employment email address for verification of reference.
• Evidence of meeting English Language requirement (if applicable).
• Copy of UK resident visa (if applicable)
• Confirmation of EDI form submission (optional) 

Informal enquiries are welcome, please contact Dr Manlio Valenti (manlio.valenti@swansea.ac.uk).

*External Partner Application Data Sharing – Please note that as part of the scholarship application selection process, application data sharing may occur with external partners outside of the University, when joint/co- funding of a scholarship project is applicable.