Geometric flows with symmetries

This project aims to understand the long-time behaviour of Ricci flows with cohomogeneity-one nilpotent symmetry. Recent breakthroughs in the Einstein case should provide the necessary tools to construct new monotone functionals and curvature estimates. 
The Ricci flow is one of the most fundamental tools in modern Differential Geometry. Understanding the behaviour of solutions that are invariant under the action of a nilpotent Lie group is of particular significance, as they model the asymptotics of the collapsing `thin parts' of arbitrary solutions with bounded curvature. These solutions are well-understood in the case of a transitive action, thanks to work of J. Lauret. The following case in terms of complexity is that of solutions with an isometric action with a one-dimensional quotient: the so-called cohomogeneity-one manifolds.

This is an Earmarked scholarship project that aligns with a recently awarded Australian Government grant.

The scholarship includes:

• living stipend of $35,000 per annum tax free (2024 rate), indexed annually
• your tuition fees covered
• single overseas student health cover (OSHC).

Learn more about the Earmarked scholarship.

You must contact the principal supervisor for this project to discuss your interest. You should only complete the online application after you have reached agreement on supervision.

Always make sure you are approaching your potential supervisor in a professional way. We have provided some guidelines for you on how to contact a supervisor.

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 Riemannian geometry, Lie groups, geometric analysis, PDEs would be of benefit to someone working on this project.

You will demonstrate academic achievement in the field of Mathematics and the potential for scholastic success.

A background or knowledge of Differential Geometry is highly desirable.

This project requires candidates to commence no later than Research Quarter 1, 2025. To allow time for your application to be processed, we recommend applying no later than 30 September, 2024 30 June, 2024.

You can start in an earlier research quarter. See application dates.

Before you apply

1. Check your eligibility for the Doctor of Philosophy (PhD).
2. Prepare your documentation.
3. Contact Dr Ramiro Lafuente (r.lafuente@uq.edu.au) to discuss your interest and suitability.

When you apply

You apply for this scholarship when you submit an application for a PhD. You don’t need to submit a separate scholarship application.

In your application ensure that under the ‘Scholarships and collaborative study’ section you select:

• My higher degree is not collaborative
• I am applying for, or have been awarded a scholarship or sponsorship
• UQ Earmarked Scholarship type.

Apply now