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

Outline

Symmetries in Nature have fascinated the mankind ever since the beginning of civilization, since they help us understanding its most fundamental laws. An easy instance is rotational symmetry, invariance of a phenomenon if we observe it independent of the viewing angle.

The more uncommon a symmetry is, the more interesting it is from a physics point of view and more exotic and original mathematical structures describe them. In the last decades there has been a substantial effort to understand those related to conformal symmetry, a symmetry particularly rare which preserves angles (but not e.g. sizes). These advances have constituted an active, rich and cutting-edge field of world-wide research.

This PhD project will study systematic ways of detecting and classifying certain algebraic structures arising in this setting and describing certain physical entities, in particular algebra objects in modular tensor categories obtained from representations of vertex operator algebras. These objects have a beautiful physical description and are connected to other mathematical formalizations of physical theories like e.g. r-spin topological field theories. These connections will also be explored during the PhD project.

To achieve these aims, the candidate will get a solid background on advanced algebra:

-representation theory,

-category theory,

-as well as the connection to the mathematical descriptions of physical aspects of conformal field theory.

Learning how to program in Sage is also to be expected, and will play a role in the development of the research project.

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

What is funded

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.

Eligibility

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.

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.