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

   School of Mathematics and Computer Science

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  Dr Manlio Valenti  No more applications being accepted  Funded PhD Project (Students Worldwide)

About the Project

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)


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. 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. 

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. 


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. 

Computer Science (8) Mathematics (25)

Funding Notes

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.

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