On multi-dimensional continued fractions

Outline

In a recent breakthrough, a particular multi-dimensional analogue of the two-dimensional continued fraction algorithm has been established by Lettington and his collaborators, which incorporates and extends the normal continued fraction construction of convergents to a point (x1,...,xm)∈Rm.

With the context briefly outlined, we can now state the main aim of this PhD project, which is to establish analytic bounds for the accuracy of the convergents for the multi-dimensional continued fraction algorithm, alongside exploring geometric properties of lattice point constructions for these convergents.

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.

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.