Number theory; on multi-dimensional sequences of convergents
This research project is in competition for funding with one or more projects available across the EPSRC Doctoral Training Partnership (DTP). Usually the projects which receive the best applicants will be awarded the funding. Find out more information about the DTP and how to apply.
Application deadline: 15 March 2019
Start date: 1 October 2019
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.
We run a successful weekly seminar series attended by all PhD students and we belong to the MAGIC Postgraduate Taught Course Consortium, for which we have provided courses in Functional Analysis and Spectral Theory. The group has organised programmes at the Isaac Newton Institute in Cambridge and has strong connections within GW4, in particular with Bath.