PhD Studentship in Pure Mathematics: The Algebraic Topology of Dynamical Systems

Award Summary

100% of home tuition fee, and a minimum tax-free annual living allowance of £17,668 (2022-23 UKRI rate).

Overview

The Algebraic Topology of Dynamical Systems

In classical algebraic topology one studies topological spaces by constructing algebraic invariants for them. This allows us to decide whether two spaces are the same, or fundamentally different. In some cases, one can even use these invariants for a complete classification.

This project will focus on the study of topological dynamics using similar ideas. The simplest example of a topological dynamical system is a homeomorphism on a compact space. Again, it turns out that sometimes one can completely classify these homeomorphisms using a certain group associated with the homeomorphism. Interestingly, the proof of this result relies heavily on methods from operator algebras, a branch of functional analysis. The interactions between the fields of topological dynamics, operator algebras, and topology exhibited in the example above have recently gained a lot of attention and have informed significant progress.

In this project the successful candidate will further develop the available toolkit of algebraic invariants for topological dynamical systems and investigate its applications to and interactions with other areas in pure mathematics. The theme of this research allows for many feasible research problems depending on the interests and strengths of the candidate. It has the potential to contribute to long-standing open problems in all the areas outlined above.

Number of awards: 1

Start date: 18^th September, 2023

Award duration: 42 months

Sponsor

School of Mathematics, Statistics and Physics, Newcastle University 

Supervisors

Dr Christian Bönicke

Eligibility criteria

You must have, or expect to gain, a minimum 2:1 Honours degree or international equivalent in a relevant subject such as Mathematics, Statistics, or another strongly quantitative discipline. Enthusiasm for research, the ability to think and work independently, excellent analytical skills and strong verbal and written communication skills are also essential requirements.

Home and international applicants (inc. EU) are welcome to apply. In the first instance the studentship covers only home tuition fees. The School of Mathematics, Statistics and Physics has very limited additional funding to offer full studentships including international fees to exceptional international applicants. Applicants whose first language is not English require an IELTS score of 6.5 overall with a minimum of 5.5 in each subsection. 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 Questions’ section:

• A ‘Personal Statement’ (this is a mandatory field) - upload a document or write a statement directly in to the application form
• The studentship code MSP061 in the ‘Studentship/Partnership Reference’ field
• When prompted regarding 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.

Contact details

Contact the supervisor for project specific information. Contact maths.physics.pg@newcastle.ac.uk for general information on applications.

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