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Holomorphic Representations of the Braid Group

  • Full or part time
  • Application Deadline
    Friday, March 15, 2019
  • Competition Funded PhD Project (European/UK Students Only)
    Competition Funded PhD Project (European/UK Students Only)

Project Description

The braid group can be intuitively understood as the collection of a finite number of strands with all possibilities of "braiding" them, and consecutive braiding as the group operation.

This group appears in many different areas in mathematics. From its description, it is not surprising that it is relevant in knot theory. But braid groups and related algebraic concepts also appear in areas where one might not expect them, such as operator algebras, quantum field theory, or in the mathematical description of lattice systems, and have contributed to the invention of new mathematical structures such as Hopf algebras.

In applications, one is often interested in representations of braid groups, i.e. realizations of the braiding relations by linear operators on some vector space. Inspired by situations encountered in quantum field theory, a particular class of (infinite-dimensional) representations takes place on Hilbert spaces of holomorphic functions, where the entirely algebraic braid group comes into contact with concepts from (complex and functional) analysis.

The project will deal with certain "holomorphic" representations of braid groups and study the dependence on an underlying "R-matrix". Depending on the interests of the student, there are possibilities to put the emphasis abstract aspects or on applications.

Funding Notes

The studentship is funded through the EPSRC Doctoral Training Partnership. It consists of full UK/EU tuition fees, as well as a Doctoral Stipend matching UK Research Council National Minimum.

UK Research Council eligibility conditions apply
To be eligible for the full award, EU Nationals must have been in the UK for at least three years prior to the start of the course for which they are seeking funding, including for the purposes of full-time education.

References

Applicants should submit an application for postgraduate study via the online application service for October 2019

In the research proposal section of your application, please specify the project title and supervisors of this project and copy the project description in the text box provided. In the funding section, please select "I will be applying for a scholarship / grant" and specify that you are applying for advertised funding from EPSRC DTP.

If are applying for more than one Cardiff University project please note this in the research proposal section.

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)

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