About the Project
To give a flavour of the type of questions involved, suppose there is a given number of people, each individual owns a piece of land and their total land mass covers the earth. Everyone shall make a precise “curvature map” of their piece of land; where are flat/bumpy, inward/outward curved pieces? This is described in terms of numbers; “flat” would be labelled zero, “curved inward” by a negative and “curved outward” by a positive number. Suppose every spot of each person’s property is measured this way. Afterwards all individuals collect their data. The key problem is: Can you determine the earth’s shape from that information?
The approach that will be pursued relies on recent developments on the bridge between Spectral Theory, Hypersurface Geometry and Partial Differential Equations (PDE), developed by the first supervisor Dr Julian Scheuer (JS) in collaboration with leading experts in Geometric Analysis. The second local supervisor Dr Federica Dragoni (FD) complements this expertise with perspectives from Stochastic Analysis.
Prof Dr Chao Xia (CX), a leading expert on Geometric Analysis in China and long-term collaborator of JS at Cardiff’s partner university at Xiamen in China, completes the supervisory team.
The student will benefit from the partnership of Cardiff University with Xiamen University in China through regular virtual exchange with CX’s research group and optional personal visits hosted by CX. During such visits, access to local seminars in Fujian province will allow the student to interact directly with world-leading experts in the relevant fields.
Cardiff University provides a highly inspiring research environment for postgraduates. Its Analysis group comprises internationally leading experts in pure and applied mathematics. Local seminars on PDE will be highly beneficial to undertake this project. The student will automatically join Cardiff’s Doctoral Academy with opportunities to interact with fellow postgraduate students from other disciplines, build networks and receive further training to attain professional skills.
HOW TO APPLY
Applicants should apply through the Cardiff University online application portal, for a Doctor of Philosophy in Mathematics with an entry point of October 2021
In the research proposal section of your application, please specify the project title and supervisors of this project.
There is no requirement to submit a research proposal
In the funding section, please select "I will be applying for a scholarship / grant" and specify that you are applying for advertised funding from EPRSC DTP.
The 3.5 year studentship includes UK fees, stipend (amount for 2020/21 is £15285) and a research training grant to cover costs such as research consumables, training, conferences and travel.
The studentship includes home UKRI fees, stipend and training support grant.
Shortlisted candidates will be invited to attend an interview w/c 22 March 2021
A 1st or upper 2nd class UK Honours degree (or equivalent) and/or a Master’s degree is required in mathematics or a 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. Further acceptable qualifications can be found at www.cardiff.ac.uk/study/international/english-language-requirements/postgraduate
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