PhD Studentship: Generalisations of Khovanov Homology and their Applications

Award summary

100% fees covered, and a minimum tax-free annual living allowance of £19,237 (2024/25 UKRI rate). Additional project costs will also be provided.

Overview

Low-dimensional topology is the study of 3- and 4-dimensional spaces, and knotted objects within such spaces. Khovanov homology is a central tool in low-dimensional topology: most basically it associates a vector space to a collection of knotted loops in 3-dimensional space. From this starting point flow a huge variety of algebraic and geometric applications. This project will explore generalising the classical Khovanov construction to new settings,and putting such generalisations to use in algebraic and geometric applications.

Number of awards: 1

Start date: 1^st October 2025

Award duration: 4 years

Sponsor: EPSRC

Supervisors: Dr William Rushworth

Eligibility criteria

A minimum 2:1 Honours degree or international equivalent in a subject relevant to the proposed PhD project (such as mathematics or theoretical physics) is our standard entry, however we place value on prior experience, enthusiasm for research, and the ability to think and work independently. Excellent Analytical skills and strong verbal and written communication skills are also essential requirements. A Masters qualification is not required if you have a minimum 2:1 degree or can evidence alternative experience in a work or research-based project. If you have alternative qualifications or experience, please contact us to discuss.

For EPSRC DLA applications we are following the EDEPI competency-based framework. Please read and complete this document as your Personal statement, and upload this with your application. Applications which do not include this document will not be considered. Further details can be found here.

Home and international applicants (inc. EU) are welcome to apply and if successful will receive a full studentship. Applicants whose first language is not English require an IELTS score of 6.5 overall with a minimum of 5.5 in all sub-skills.

International applicants may require an ATAS (Academic Technology Approval Scheme) clearance certificate prior to obtaining their visa and to study on this programme. 

How to apply

You must apply through the University’s Apply to Newcastle Portal

Once registered select ‘Create a Postgraduate Application’.

Use ‘Course Search’ to identify your programme of study:

• Search for the ‘Course Title’ using the programme code: 8080F
• Research Area: Pure Mathematics
• Select ‘PhD Mathematics (full time) - Pure mathematics' as the programme of study

You will then need to provide the following information in the ‘Further Details’ section:  

• A ‘Personal Statement’ (this is a mandatory field) – Use this template
• The studentship code DLA2501 in the ‘Studentship/Partnership Reference’ field
• When prompted for how you are providing your research proposal - select ‘Write Proposal’. You should then type in the title of the research project from this advert. You do not need to upload a research proposal

You must submit one application per studentship, you cannot apply for multiple studentships on one application

Contact details

Dr William Rushworth, william.rushworth@ncl.ac.uk You can also contact: doctoral.awards@ncl.ac.uk for independent advice on your application.

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