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EPSRC DTP studentship in Algebraic structures in mathematical physics and category theory


Project Description

Symmetries in nature have fascinated mankind ever since the beginning of civilization, as they help us understanding nature’s most fundamental laws. A familiar example is rotational symmetry: the fact that physical phenomena do not depend on the direction they are observed from.

The symmetries something admits the more exotic and rich the associated mathematical structures become and therefore the more solvable the associated physical phenomena become.
In recent decades there has been a substantial effort to understand conformal symmetry: the invariance under coordinate transformations which preserve angles but not necessarily lengths. The field as a whole has come to be knowns as conformal field theory.

This PhD project is on the interface between pure mathematics and mathematical physics. It will study ways of detecting and classifying certain algebraic structures arising in this setting, in particular algebra objects in modular tensor categories obtained from representations of vertex operator algebras. These structures encode concepts from physics in elegant ways and interconnect a number of mathematical formalisations of physical theories such as r-spin topological field theories. Exploring these connections will form a vital part of the PhD project.

To achieve these aims, the student will develop a solid background in advanced algebra:
• representation theory,
• category theory,
• the relations between the various mathematical descriptions of conformal field theory.

The project will have a programming component which will give the student the opportunity to learn the Sage and Python programming languages.

Additionally, the student will get additional training on academic skills such as critical thinking and logical reasoning, scientific writing and communication, research independence, and collaboration. They will become part of an international network of researchers, and are expected to produce scientific output in the shape of publications, talks and conference posters.

The 3.5 year studentship includes UK/EU fees, stipend (amount for 2020/21 is £15285) and a research training grant to cover costs such as research consumables, training, conferences and travel.

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 2020
In the research proposal section of your application, please specify the project title and supervisors of this project. 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.
Shortlisted candidates will be invited to attend an interview in April

If you have any questions please contact Dr. Ana Ros Camacho (roscamachoa _at_ cardiff.ac.uk) or Dr. Simon Wood (woodsi _at_ cardiff.ac.uk) for any inquiries regarding the position. If you are interested in applying for this position, please tell us about your scientific interests, any relevant lectures you have taken previously, and why you are interested in this particular project specifically. We look forward to hearing from you!

Funding Notes

ELIGIBILITY CRITERIA
UK/EU applicants only. UK Research Council eligibility conditions apply

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 6.0 in each skills component. Further acceptable qualifications can be found at View Website

References

A suitable candidate will have a Degree and Master in Pure Mathematics or related areas. Prior knowledge or previous projects on this research topic are a plus. Female and minority candidates are particularly encouraged to apply.

Relevant reading material
The following are a list of textbooks which you can consult to get a feel for some of the mathematics involved in this project.
• Monoidal Categories and Topological Field Theory, Turaev and Virelizier
• Vertex Algebras for Beginners, Kac,
• Conformal Field Theory, Di Francesco, Mathieu and Sénéchal


Related Subjects

How good is research at Cardiff University in Mathematical Sciences?

FTE Category A staff submitted: 24.05

Research output data provided by the Research Excellence Framework (REF)

Click here to see the results for all UK universities

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