Manifold approximation in higher dimensions

Project description

While computational topology has provided tools for understanding scalar and bivariate fields, many simulations generate large numbers of variables, resulting in fields of the form R^n -> R^m where m > n. These cases are harder to attack with Reeb / fiber analysis, which is  well-defined only for m <= n. However, the domain of the function is most typically R^4 at the most (i.e. n = 4), and its graph is therefore an n-manifold embedded in an (m+n) space. This imposes strong limitations on the portion of the embedding space or range that include data values, and the Joint Contour Net approach to analysis results in a rasterisation of the input data into the range. 

This project will seek to explore the use of quantised approximations of the function's graph to determine interesting features in the data.

Entry requirements

Applications are invited from candidates with a minimum of a UK upper second class honours degree (2:1), and/ or a Master's degree in a relevant subject. We also recognise relevant industrial and academic experience.

How to apply

Formal applications for research degree study should be made online through the university's website. Please state clearly in the research information section of your application, the name of the PhD you wish to apply for is 'Manifold approximation in higher dimensions' as well as Dr Hamish Carr as your proposed supervisor. In the funding section, please state 'School of Computing Funded Studentships' as your sponsor.

If English is not your first language, you must provide evidence that you meet the University’s minimum English Language requirements.

We welcome scholarship applications from all suitably-qualified candidates, but UK black and minority ethnic (BME) researchers are currently under-represented in our Postgraduate Research community, and we would therefore particularly encourage applications from UK BME candidates.  All scholarships will be awarded on the basis of merit.

If you require any further information please contact the Graduate School Office
e:, t: +44 (0)113 343 8000.