Applications are invited for a self-funded, 3-year full-time or 6-year part time PhD project.
The PhD will be based in the School of Mathematics and Physics, and will be supervised by Dr Ittay Weiss.
The work on this project could involve:
- Development of new mathematical foundations motivated by data analysis needs.
- Utilisation of category theoretic techniques in modelling.
- Elucidation of topological data analysis tools via a sound mathematical framework.
- Creation of new algorithms based on constructive categorical principles.
Project description
Recent years have seen rapid expansion in data analysis challenges. Often, the standard techniques of mathematics yield little to no satisfactory results, necessitating new approaches. An approach that is increasing in popularity employs category theory as the underlying mathematics. Category theory is a powerful language that leads to constructive mathematical arguments which are translatable into algorithms. The project aims to provide a sound mathematical foundation for data analysis, drawing inspiration from topological data analysis and clustering theory.
In recent work carried out by Dr Ittay Weiss at the University of Portsmouth a foundation of topology was given which makes use of constructively completely distributive lattices. This formalism is mathematically equivalent to the classical one, but its language directly leads to computable interpretations. This is an aspect of the general philosophy of the project, an aim of which is to utilise this new formalism for topology in order to extend existing topological data analysis techniques. In particular, the lattice-theoretic approach suggests new ways to tackle multiparameter persistent homology.
Clustering theory is an area of data analysis for which a single unifying mathematical foundation is desirable, but unknown. In the past 20 years categorical attempts have been made to provide such a foundation, with some success. An aim of the project is to use enriched category theory in order to provide a sound foundation for clustering theory. Clustering is seen as a special form of change of enrichment. The development of that angle motivates adapting existing algorithms that compute Kan extensions to the enriched context. Such extensions are expected to lead to new clustering methods, while the underlying foundation would provide sound tools for comparison of different methods.
Existing knowledge of category theory is not required. Sufficient comfort with proof-based mathematics is required, as is willingness to develop fluency in category theory.
General admissions criteria
You'll need a good first degree from an internationally recognised university 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.
Specific candidate requirements
Familiarity with category theory would be a plus, but is not a prerequisite. Familiarity with proofs in mathematics is required at a level of comfort, but no specific techniques are required. Willingness to develop fluency in category theory, if needed, is expected which could last for the first year.
How to Apply
We encourage you to contact Dr Ittay Weiss ([Email Address Removed]) to discuss your interest before you apply, quoting the project code.
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.
When applying please quote project code:SMAP5721023.
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