Number Theory; On Multi-Dimensional Sequences of Convergents

Outline

This project is centred on constructions and limits of sequences of vector convergents, systems of polynomials and generating function matrices, including the application of special function theory.

There are a number of possible directions within this project as there are currently many areas that are of interest from description/categorisation theories to general unifying approaches and extensions of current methodologies.

Project aims and methods

You will learn about ideas from number theory, combinatorics and mathematical analysis, including special function theory. The project will involve an element of numerical analysis via Mathematica.

This is a project in pure mathematics. The most likely outcome is two or three papers in good journals. If you are very good then we would aim to submit an EPSRC responsive mode PDRA grant application to continue the research, with the new PhD as the named PDRA.

The Mathematical Analysis Group, incorporating the Number Theory Group, is the largest research group in the School of Mathematics and currently holds sizeable EPSRC grants. It has continuous EPSRC funding going back over ten years and has had EPSRC postdoctoral fellows, an EPSRC Research Fellow, a Marie Curie Fellow and a Swiss National Foundation Fellow. The School’s only applicant for a Marie Curie COFUND Fellowship in the current round comes from this group.

What is funded

Self-funded students only.

How to Apply

Applicants should submit an application for postgraduate study via the online application service: http://www.cardiff.ac.uk/study/postgraduate/research/programmes/programm...

In the research proposal section of your application, please specify the project title and supervisors of this project and copy the project description in the text box provided.

In the funding section, please select the ’self -funding’ option and specify the project title

We are interested in pursuing this project and welcome applications if you are self-funded or have funding from other sources, including government sponsorships or your employer.