EPSRC DTP PhD studentship in Operator algebras and quantum graphs

Operator algebras and quantum graphs

The primary goals of this project are to explore quantum graphs and their applications to operator algebras, and to develop techniques of non-commutative combinatorics. In quantum graphs, the nxn matrices become “non-commutative functions” on n “non-commutative points”, which are then equipped with an adjacency matrix analogue. 

Quantum graphs form the basis of an exciting area of ongoing research. Their original applications lie in quantum information theory, but they have now found applications within operator algebras: for example, they are linked to the recently-resolved Connes’ Embedding Problem–the question of whether a class of von Neumann algebras (so-called separable II_1 factors) can be approximated by matrices, or equivalently whether all theoretically-possible quantum systems can be approximated with finite dimensional ones. Ideas from graph theory can be interpreted here: for example, some graphs may be “quantum coloured” using fewer colours than needed to colour them in the traditional sense. There remains a wealth of unexplored ideas from graph theory; for example, there is currently no notion of quantum planarity for graphs. The objectives of this project are to investigate quantum analogues of ideas from graph theory, and to understand their operator algebraic consequences. 

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 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.

This studentship will be undertaken within the Geometry, Algebra, Mathematical Physics and Topology (GAPT) 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 operator algebras and many connected fields. 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 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.

The possible entry dates for the PhD studentship are 1 January 2025 or 1 April 2025.

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.

Shortlisted candidates will be invited to attend an interview.

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 an entry point of 1 January 2025 or 1 April 2025.

In the research proposal section of your application, please specify the project title and supervisor of this project. In the funding section, please specify that you are applying for advertised funding from the EPSRC.

In addition to the standard application form, applicants should also:

· Attach a CV. Guidance on CVs for a PhD position can be found on the FindAPhD website.

· Ensure your personal statement (as part of the university application form, or as a separate attachment, if you prefer) provides a clear explanation of your research interest, preparation undertaken, and an understanding of the project.

Your personal statement should be no more than 500 words, and address the following questions:

1. What are your scientific research interests and ambition?

2. How has your academic and/or professional journey prepared you for PhD study? (for instance, give examples of work you particularly enjoyed, of challenges you overcame, of connecting with others about your work or ideas, of showing inventiveness, of developing new skills and knowledge)

3. Why do you think this project is important?

For general information about EPSRC-funded studentships at Cardiff, please see https://www.cardiff.ac.uk/study/postgraduate/funding/research-councils/epsrc-studentships .