Project code



School of Mathematics and Physics

Start dates

February and October

Application deadline

Applications accepted all year round

Applications are invited for a 3 year PhD to commence in October 2020 or February 2021.

The PhD will be based in the Faculty of Technology, and will be supervised by Dr Ittay Weiss.

The work on this project could involve:

  • Developing new techniques in frontiers of topological data analysis
  • Synergising advanced methods of algebraic topology to facilitate new applications and enhance existing ones
  • Developing new algorithms based on metric techniques to address problems in data science

Topological Data Analysis (TDA) is an emerging and highly successful approach to Big Data problems. The underlying idea is to employ topological techniques in the analysis of large quantities of data. One of the main difficulties with real-world data is that its collection introduces various types of 'noise'. Distinguishing between true features, inherent to the phenomenon in question, and misleading features resulting from noise contamination can be very challenging. Topology, by design, is blind to matters of scale or dimensionality. Its tools are aiming to extract geometric features which are robust in comparison to scale or dimensionality distortions. TDA seeks to exploit the inherent noise-blindness of topology by employing topological techniques to data analysis.

TDA represents a unique intersection point of pure mathematics with applied mathematics. In recent work such a formalism for topology was identified and is being developed. The advantages of the formalism to the foundations of topology are demonstrated while more advanced features are being tested. Alongside the topological gains, applications to the foundations of TDA are emerging as well. The main aims of the project are: 1) further enhance and develop the new mathematical foundations of topology; and 2) investigate the flow of ideas between topology and TDA along this new bridge, with new applications of TDA in mind.

The project aims to investigate alternative formalisms of topology with the aim of facilitating a smoother transition of topological tools to TDA, thereby enlarging the scope of applicability of TDA, while at the same time adjusting the classical topological methodologies to allow insights from TDA to filter back to topology. Using this improved language and tools new algorithms will be developed and tested for tackling TDA problems.

Fees and funding

Visit the research subject area page for fees and funding information for this project.

Funding availability: Self-funded PhD students only. 

PhD full-time and part-time courses are eligible for the UK Government Doctoral Loan (UK and EU students only).

Entry Requirements Accordian Panel

  • You'll need a good first degree from an internationally recognised university (minimum second class or equivalent, depending on your chosen course) or a Master’s degree in a relevant subject area
  • 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

Familiarity with formal proof based mathematics, and in particular topology.

How to apply

When you are ready to apply, please follow the 'Apply now' link on the Mathematics PhD subject area page and select the link for the relevant intake. 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.