Distinguished geometric structures in four dimensions

Project opportunity

This Earmarked Scholarship project is aligned with a recently awarded Category 1 research grant. It offers you the opportunity to work with leading researchers and contribute to large projects of national significance.

An important problem in differential geometry is finding shapes that are somehow "better" than others. The theory of these optimal shapes is quite satisfying in dimensions two and three, but the classification problem starts to become quite challenging in dimension four. In this project, the student will use existing tools from geometric analysis, including the Ricci flow, to study the existence and uniqueness of these canonical structures on four-dimensional manifolds.

Scholarship value

As a scholarship recipient, you'll receive: 

  • living stipend of $32,192 per annum tax free (2023 rate), indexed annually
  • tuition fees covered
  • single Overseas Student Health Cover (OSHC)


Dr Timothy Buttsworth

School of Mathematics & Physics

Email: t.buttsworth@uq.edu.au

Preferred educational background

Your application will be assessed on a competitive basis.

We take into account your

  • previous academic record
  • publication record
  • honours and awards
  • employment history.

A working knowledge of differential equations, geometric analysis and numerical analysis would be of benefit to someone working on this project.

The applicant will demonstrate academic achievement in the field(s) of differential geometry and mathematical analysis and the potential for scholastic success.

A background or knowledge of Ricci flow is highly desirable.

Latest commencement date

If you are the successful candidate, you must commence by Research Quarter 1, 2024. You should apply at least 3 months prior to the research quarter commencement date.

If you are an international applicant, you may need to apply much earlier for visa requirements.

How to apply

You apply for this project as part of your PhD program application.

View application process