Topological data analysis brings tools from pure mathematics such as geometry and algebraic topology to bear on statistical problems in order to understand the structure of large data sets in high dimensions.
A common assumption is that the data set lies on or near some manifold. This project aims to develop new techniques to estimate geometric and topological properties of the manifold from the sample. In particular, we will seek to understand properties related to dimension and curvature.
The student will analyse existing techniques to better understand their pure mathematical underpinnings, test techniques in real-world applications, and develop new approaches.
This work is part of a UK Research & Innovation Future Leaders Fellowship led by Dr John Harvey. Please direct project-specific enquiries to [Email Address Removed].
WHAT WE OFFER
Cardiff's School of Mathematics provides an excellent postgraduate research environment including:
· our new purpose-built 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 OR,
· comprehensive professional skills training offered by Cardiff’s Doctoral Academy.
The PGR community is very active in running the SIAM-IMA Student Chapter, a valuable forum for exchange of ideas and public engagement.
The student will join the School’s Geometry, Algebra, Mathematical Physics and Topology group, which includes several members with interests in topological data analysis.
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 studentship includes fees, stipend at the UKRI rate and a Research Training Support Grant to cover costs such as research consumables, training, conferences and travel. Via the Future Leaders Fellowship, the student may benefit from additional funding to present work linked to the project at conferences and other meetings.
The next possible entry dates for PhD study are 1st July 2023 or 1st October 2023.
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
· Knowledge of geometry or topology (such as from advanced level modules at undergraduate level)
· A willingness to learn statistical methods and acquire programming skills
· 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.
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.
This studentship is available for UK home students only. Shortlisted candidates will be invited to attend an interview.
SUPPORTING DOCUMENTS
· Curriculum vitae
· A personal statement
· Two references
· Degree certificates and transcripts
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 July or October 2023.
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