Project code



School of Mathematics and Physics

Start dates

October 2021

Closing date

4 May 2021

Applications are invited for a fully-funded three year PhD to commence in October 2021. 

The PhD will be based in the School of Mathematics and Physics and will be supervised by Dr Ittay Weiss.

Candidates applying for this project may be eligible to compete for one of a small number of bursaries available; these cover tuition fees at the UK rate for three years and a stipend in line with the UKRI rate (£15,609 for 2021/22). Bursary recipients will also receive a £1,500 p.a. for project costs/consumables. 

The work on this project could involve:

  • Development of new algorithms for computational category theory
  • Research of new applications of category theory in data science
  • Development of new ideas in category theory to tackle emerging areas of demand

Category theory reached a highly sophisticated level of maturity and in recent years is leading a revolution offering cutting edge solutions to both existing and emerging problem domain areas. An example is the work pioneered by Dr David Spivak where category theory is used to dramatically improve  techniques of data migration and data integration in database theory. Dr David Spivak (MIT) and Dr Ryan Wisnesky (Conexus) discovered an algorithm for efficiently computing Kan extensions. The algorithm is a synergy between category theory and database theory, and is the at the heart of the commercial database services company Conexus that they founded.

The aim of the project is to continue the line of investigation of computational category theory, following several directions. Firstly, the efficient algorithm for computing Kan extensions is very new. A detailed study of it is not yet in existence and it is imperative to have a solid understanding of its strengths and weaknesses. This project aims to perform a careful analysis of the algorithm to obtain rigorous information about its performance. Second, it is well known that Kan extensions in category theory are among the most ubiquitous constructions. Many seemingly unrelated constructions can all be realised as Kan extensions. Therefore, the application of the algorithm to database theory is but one of many potential ones. The project will look into applications in topological data analysis (TDA). Current techniques in TDA are ad-hoc, but categorical in nature. A successful application of the new algorithm in TDA is both likely and of tremendous potential for impact in areas where TDA is used, which include brain research, chemistry, and material science.  

Finally, an even more vastly encompassing concept is that of enriched Kan extension. The project will seek to identify particular enrichment scenarios where the algorithm can still be used efficiently.

Entry reqs

You'll need a good first degree from an internationally recognised university (minimum upper second class or equivalent, depending on your chosen course) or a Master’s degree in an appropriate subject. In exceptional cases, we may consider equivalent professional experience and/or qualifications. English language proficiency at a minimum of IELTS band 6.5 with no component score below 6.0.

You should have basic programming skills. Some knowledge of data structures and/or functional programming would be welcomed but not required. Familiarity with category theory would be advantageous but not a prerequisite. Mathematical maturity obtained through a good degree with significant proof-based components is required as is willingness to learn category theory.

How to apply

We’d encourage you to contact Dr Ittay Weiss ( to discuss your interest before you apply, quoting the project code.

When you are ready to apply, you can use our online application form. Make sure you submit a personal statement, proof of your degrees and grades, details of two referees, proof of your English language proficiency and an up-to-date CV.  Our ‘How to Apply’ page offers further guidance on the PhD application process. 

If you want to be considered for this funded PhD opportunity you must quote project code SMAP5980521 when applying.