Sub-Riemannian Curvature flows

About the Project

In sub-Riemannian geometries, a major obstacle to study degenerate PDEs is the lack of good concavity properties of the distance function. This project aims to face the problem with a new metric regularization technique and to establish comparison principles and uniqueness for horizontal mean curvature flow.

After familiarizing with the CC distance in Carnot groups and the viscosity definition of horizontal mean curvature flow, the candidate will study horizontally semi-concavity preserving properties for the metric inf and sup convolution. This will lead to an approach to solve the uniqueness problem for a class of degenerate PDEs, e.g. horizontal mean curvature flow.

Project lead: Professor Federica Dragoni (MATHS)

Project partners: Professor Andrea Pinamonti, Universita di Trento, Italy, Qing Liu, OIST, Japan

What we offer:

Cardiff's School of Mathematics provides an excellent postgraduate research environment including:

• research facilities at Abacws (co-designed by our PGR community),
• a vibrant research culture including a wide range of research events,
• access to national course centres in mathematics, statistics and Operational Research,
• comprehensive professional skills training offered by Cardiff’s Doctoral Academy.
• collaborations with other disciplines and with a wide range of external partners (industry and society).

The PGR community is very active in running the SIAM-IMA Student Chapter, a valuable forum for exchange of ideas and public engagement.

This studentship will be undertaken within the Mathematical Analysis research group at the School of Mathematics. The group’s members have wide-ranging interests, and offer a dynamic environment for the student to engage with experts in mathematical analysis and many other fields in mathematics and other disciplines. The group hosts a weekly seminar inviting external speakers.

Completing a PhD in mathematics opens up a range of possible next steps, from continuing an academic career to working in mathematically technical roles in industry.

The 3.5 year programme does not have any funding attached but successful applicants will receive a small Research Training Support Grant to cover costs such as research consumables, training, conferences and travel.

The possible start dates for this PhD are October, January, April or July.

What you bring:

You should have a 1st or upper 2nd class UK Honours degree (or equivalent) and/or a Master’s degree in mathematics or a suitable related subject.

Applicants for whom English is not their first language must demonstrate their proficiency by obtaining an IELTS score of at least 6.5 overall, with a minimum of 5.5 in each skills component, or equivalent qualification.

Cardiff University is committed to supporting and promoting equality and diversity and to creating an inclusive research environment. We particularly welcome applications from underrepresented groups.

How to apply:

Applicants should apply through the Cardiff University online PhD application portal, for a Doctor of Philosophy in Mathematics with your desired entry point.

You must include

• Transcript(s) of your degree(s) (with certified translations if appropriate)
• Degree certificates (with certified translations if appropriate)
• References - these should be current and verifiable
• Personal statement (as part of the university application form, or as a separate attachment, if you prefer) this should provide a clear explanation of your research interest, preparation undertaken, and an understanding of the project.

Note that the 'register interest' option will not submit an application. Please follow the instructions above and submit your application via our online portal. Incomplete applications will not be considered.