Topics in Fractal Geometry (Ref: SCI25-SB)

The goal of this project is to deepen our understanding of invariant sets and measures arising from iterated function systems. This goal can be approached from various perspectives. Specific problems include understanding the cardinality and complexity of the set of codings for a point in the invariant set, and bounding the Fourier transform of stationary measures. This project combines ideas from Ergodic Theory, Fractal Geometry, and Number Theory.

Please look at my list of publications and recent presentations (available at my personal homepage) to get a feel for possible areas of research.

This project will provide an opportunity to work with world leading experts and to take part in cutting edge research. The successful applicant will have the opportunity to travel to attend conferences, and to develop the necessary skills for a career in academia.

Loughborough University is a top-ten rated university in England for research intensity (REF2014). In choosing Loughborough for your research, you’ll work alongside academics who are leaders in their field. You will benefit from comprehensive support and guidance from our Graduate School, including tailored careers advice, to help you succeed in your research and future career.

Supervisor:

• Simon Baker

Entry requirements:

Applicants should have, or expect to achieve, at least a 2:1 Honours degree (or equivalent) in Mathematics or a related subject. A relevant Master’s degree and/or experience in Pure Mathematics will be an advantage.

English language requirements:

Applicants must meet the minimum English language requirements. Further details are available on the International website.

Funding information:

The studentship is for 3 years and provides a tax-free stipend of £19,237 per annum for the duration of the studentship plus university tuition fees.

Please note that studentships will be awarded on a competitive basis to applicants who have applied to this project and other advertised projects starting with advert reference ‘SCI25-’ in the School of Science. Successful candidates will be informed during April 2025.

How to Apply:

All applications should be made online. Under programme name, select ‘Mathematical Sciences’. Please quote the advertised reference number: ‘SCI25-SB’ in your application. 

To avoid delays in processing your application, please ensure that you submit a CV and the minimum supporting documents. 

The following selection criteria will be used by academic schools to help them make a decision on your application. 

Project search terms:

mathematics, pure mathematics, Fractal Geometry

Email Address Science: Sci-pgr@lboro.ac.uk