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PhD studentship in Pure Mathematics- Representation Theory and Tensor Categories

Newcastle University

Qualification Type: PhD
Location: Newcastle upon Tyne
Funding for: UK Students, EU Students, International Students
Funding amount: £18,662
Hours: Full Time
Placed On: 11th December 2023
Closes: 31st January 2024
Reference: MSP079

Award Summary

100% of home tuition fees covered and a minimum tax-free living allowance of £18,622 (2023-24 UKRI rate).  

Overview

Representation Theory and Tensor Categories 

The category of finite dimensional representations of a group or an affine group scheme or a quantum group is a tensor category. One would like to understand the fusion rules that describe the decomposition of tensor products or one seeks qualitative information like the classification of tensor ideals or the connection to other categories via tensor functors. 

 

I am particularly interested in the following two research areas.  

1) Algebraic supergroups and Lie superalgebras generalize the notions of algebraic groups and Lie algebras. The general linear group generalizes to the general linear supergroup and the orthogonal and symplectic group simultaneously to the orthosymplectic supergroup. The tensor structure of the representation categories is widely unknown. In a project in this area the successful candidate would study various ways to understand the tensor structure via categorical techniques, character formulas or homotopical algebra. 

2) Deligne categories are families of universal tensor categories that interpolate other representation categories. For example, representations of the symmetric group can be extended to complex parameters. In a project in this area the successful candidate would further develop this theory, in particular by comparing them to other categories which capture the phenomenon of stabilization with respect to rank.  

Number Of Awards

1

Start Date

16th September 2024 

Award Duration

3.5 years 

Application Closing Date

31 January 2024 

Sponsor

School of Mathematics, Statistics and Physics, Newcastle University

Supervisors

Dr Thorsten Heidersdorf, School of Mathematics, Statistics, and Physics 

Eligibility Criteria

This studentship is in the first instance available to home students (UK students and EU students with settled or pre-settled status) who have or expect a first class or high 2:1 honours degree in [Mathematics / Statistics / Physics] or another relevant discipline. A Masters qualification in a relevant subject area is advantageous. Exceptional international/EU applicants will also be considered.  

Applicants whose first language is not English require a minimum of IELTS 6.5. International applicants may require an ATAS (Academic Technology Approval Scheme) clearance certificate prior to obtaining their visa and to study on this programme. 

How To Apply

To apply for a studentship, you must register and apply through the University’s Apply to Newcastle Portal 

Once registered select ‘Create Application’ and then ‘Postgraduate’. 

Use ‘Search Course’ to identify your programme of study: 

  • you can search for the ‘Course Title’ using the programme code: 8080F 
  • in the 'Research Area' field select 'Pure Mathematics'
  • select PhD Mathematics (full time)’ as the programme of study 

You will then need to provide the following information in the ‘Further Details’ section: 

  • a ‘Personal Statement’ (this is a mandatory field) - upload a PDF document or write a statement directly in to the application form (one-page in length)
  • a ‘Research proposal’ (this is a mandatory field) – upload as a PDF document (max 1 side of A4) describing your previous/ongoing experience and research interests 
  • the studentship code MSP079 in the ‘Studentship/Partnership Reference’ field 

In the ‘Supporting Documentation’ section please upload: 

  • a ‘Curriculum Vitae’ (this is a mandatory field) - upload as a PDF document (max 2 sides of A4) 

Contact Details

For more information about the possible research topics contact Thorsten Heidersdorf via email thorsten.heidersdorf@newcastle.ac.uk. For general application enquires please contact MSP PGR Support and email maths.physics.pg@newcastle.ac.uk

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