Fully Funded EPSRC and Swansea University PhD Scholarship: Effective Dimensions: Applications of Computability Theory to Geometric Measure Theory

Swansea University

Funding suppliers: EPSRC and Swansea College’s School of Science and Engineering

Topic areas: Computability principle, computable evaluation, geometric measure principle, efficient descriptive set principle

Challenge description: 

Current works confirmed how instruments from computability principle and computable evaluation can be utilized to check the geometric properties of units. Specifically, the Level-to-Set Precept supplies an express connection between the Hausdorff dimension of a set (a notion of basic significance in evaluation and geometric measure principle) and the Kolmogorov complexity of its factors (a computability-theoretical notion that measures the “(in)compressibility” of a string). This resulted in a brand new wave of outcomes, each in computability principle and in different areas of arithmetic, and a few theorems in geometric measure principle have been confirmed, for the primary time, utilizing these instruments.

The search for point-to-set ideas might be condensed into the query “If a set has a sure structural/topological property, what are the computability-theoretical traits of its factors?”. The objective of this undertaking is to strengthen the connection between computable evaluation and “classical” arithmetic, and exploring computability-theoretical notions have an effect on the geometric construction of units.

This undertaking is of course linked with a number of subjects in theoretical pc science and arithmetic, together with after all computability principle and geometric measure principle, but in addition (efficient) descriptive set principle, harmonic evaluation, and algorithmic info principle. The best candidate would have a powerful background in arithmetic, theoretical pc science, or associated subjects. Prior publicity to (a few of) the above subjects is most well-liked however not required.


Candidates should maintain an undergraduate diploma at 2.1 stage in Pc Science, Arithmetic or a intently associated self-discipline, or an acceptable grasp’s diploma with a minimal total grade at ‘Benefit’ (or Non-UK equal as outlined by Swansea College). If you’re eligible to use for the scholarship (i.e. a pupil who’s eligible to pay the UK price of tuition charges) however don’t maintain a UK diploma, you’ll be able to examine our comparability entry necessities. Please notice that you could be want to offer proof of your English Language proficiency.

English Language: IELTS 6.5 Total (with no particular person element under 6.0) or Swansea College recognised equal.

This scholarship is open to candidates of any nationality.

Please go to our web site for extra info on eligibility.


This scholarship covers the complete price of tuition charges and an annual stipend at UKRI price (at the moment £18,622 for 2023/24).

Further analysis bills will even be obtainable. 

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