|Location:||Newcastle upon Tyne|
|Funding for:||UK Students, EU Students, International Students|
|Placed On:||5th December 2022|
|Closes:||3rd February 2023|
100% of home tuition fee, and a minimum tax-free annual living allowance of £17,668 (2022-23 UKRI rate).
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: 18th September, 2023
Award duration: 42 months
School of Mathematics, Statistics and Physics, Newcastle University
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:
You will then need to provide the following information in the ‘Further Questions’ section:
Contact the supervisor for project specific information. Contact email@example.com for general information on applications.
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