Free-Discontinuity Problems and Perimeter Inequalities under Symmetrisation (2019)

What you get

You will receive:

• fully funded tuition fees for 3 and a half years (at the UK/EU rate)
• a tax-free bursary for living costs for 3 and a half years. For 2018/19 this is £14,777 per year.
• funds for computing, books, open access publishing, attendance at conferences and workshops.

You may also supplement your income with paid teaching (with your supervisor’s agreement).

Type of award

Postgraduate Research

PhD project

Supervisor: Dr Filippo Cagnetti

A fully-funded 3-and-a-half year PhD position is available in the Department of Mathematics in the School of Mathematical and Physical Sciences at the University of Sussex.

Free-discontinuity problems were introduced by Ennio De Giorgi and Luigi Ambrosio in 1988. 

These are variational problems where the energy to be minimised involves both volume and surface terms. The expression “free-discontinuity” refers to the fact that the set where the surface energy is concentrated is not a priori fixed, and can be described as the discontinuity set of a function. Applications for the theory of free-discontinuity problems range from image segmentation, to fracture mechanics, to the study of liquid crystals.

The natural framework for such problems is that one of SBV functions, i.e. Special functions of Bounded Variation. Roughly speaking, these functions are allowed to be discontinuous on a surface, but they still admit a distributional derivative, which is a “regular” measure.

In some applications, the more general class of SBD functions can be considered (Special functions of Bounded Deformation).

The case when the energy only consists of a surface term is also very interesting and includes, for instance, the (anisotropic) perimeter functional. Possible topics for this project are:

• deterministic and/or stochastic homogenisation of free-discontinuity problems  
• studying the effect of symmetrisation on perimeter functionals

Eligibility

To be eligible, you must:

• be a UK/European Union (EU) student.
• have or expect to have a UK undergraduate/master’s degree, or equivalent, in Mathematics or equivalent 
• Meet the English langugage requirement as detailed here: https://www.sussex.ac.uk/study/phd/degrees/mathematics-phd 

Deadline

31 July 2019 12:00

How to apply

Apply through the postgraduate application system and select the full time PhD in Mathematics with a September 2019 start date, depending on your availability. 

Applications will be considered until the position has been filled.

When you apply, you should include:

• the supervisor’s name (Dr Filippo Cagnetti) in the ‘Suggested supervisor’ section
• Free-Discontinuity Problems and Perimeter Inequalities under Symmetrisation in the ‘Award detail’ section
• a research proposal/personal statement which describes your suitability for the project
• 2 academic references
• your transcripts from any previously obtained degrees. If you have not yet completed your undergraduate degree, you can provide an interim transcript or record of any marks obtained so far.

The position will be filled as soon as a suitable candidate is found so you are encouraged to apply as soon as you are able to. 

Due to the high volume of applications received, you may only hear from us if your application is successful.

Contact us

Email Dr Filippo Cagnetti (F.Cagnetti@sussex.ac.uk) if you have a question about the project

Email mpsresearchsupport@sussex.ac.uk if you have a question about applying, funding or eligibility.