Postdoctoral Research Associate in Pure Mathematics

Durham, United Kingdom
£33,797 per annum
21 Dec 2020
End of advertisement period
18 Jan 2021
Contract Type
Fixed Term
Full Time

Department of Mathematical Sciences

Grade 7: - £33,797 per annum
Fixed Term - Full Time
Contract Duration: 3 years
Contracted Hours per Week: 35
Closing Date: 18-Jan-2021, 7:59:00 AM 

Durham University

Durham University is one of the world's top universities with strengths across the Arts and Humanities, Sciences and Social Sciences. We are home to some of the most talented scholars and researchers from around the world who are tackling global issues and making a difference to people's lives.

The University sits in a beautiful historic city where it shares ownership of a UNESCO World Heritage Site with Durham Cathedral, the greatest Romanesque building in Western Europe. A collegiate University, Durham recruits outstanding students from across the world and offers an unmatched wider student experience.

Less than 3 hours north of London, and an hour and a half south of Edinburgh, County Durham is a region steeped in history and natural beauty. The Durham Dales, including the North Pennines Area of Outstanding Natural Beauty, are home to breathtaking scenery and attractions. Durham offers an excellent choice of city, suburban and rural residential locations. The University provides a range of benefits including pension and childcare benefits and the University’s Relocation Manager can assist with potential schooling requirements.

Durham University seeks to promote and maintain an inclusive and supportive environment for work and study that assists all members of our University community to reach their full potential. Diversity brings strength and we welcome applications from across the international, national and regional communities that we work with and serve.

The Department

The Department of Mathematical Sciences is one of the UK’s best Mathematics departments with an outstanding reputation in teaching, research and employability of our students. Ranked 7th in terms of grade point average intensity in the Research Excellence Framework 2014, it has an active programme of internationally recognized research in Pure Mathematics, Applied Mathematics (including Applied Analysis and PDE, Theoretical Particle Physics and Mathematical Biology) and Statistics and Probability. The research culture is vibrant, with many visitors, seminars, international conferences and workshops. We aim to provide a supportive and friendly environment with a strong sense of community. The Department, which currently has 88 permanent members of staff, is set to grow significantly over the next ten years, and in 2021 we will move into a brand new building.

The Department holds an Athena SWAN Bronze award. Athena SWAN is a national initiative that recognises the advancement of gender equality, representation, progression and success for all in academia. The Department also supports the London Mathematical Society Good Practice Scheme, whose aim is to support mathematics departments to embed equal opportunities for women within their working practices.

Durham University is committed to the Concordat to support the career development of researchers. For further information please visit the Research Staff web pages on http://www.dur.ac.uk/hr/researchstaff

The Role

 Applications are invited for a Postdoctoral Research Associate in Pure Mathematics. The position is funded by the ERC Starting Grant of Michael Magee (the Principal Investigator) titled `The ubiquity of optimal spectral gaps’ (UBIQGAP, no. 949143). An abridged abstract of the program follows.

Spectral gap is a fundamental concept in mathematics, physics, and computer science as it governs the exponential rate at which a process converges towards its stationary state. It informs the spectral lines of hydrogen, how we shuffle cards, the behaviour of semiconductors, and web search algorithms. Moreover, some of the most prominent issues of contemporary mathematics, including the Ramanujan-Petersson conjecture and the Yang-Mills mass gap, revolve around spectral gap. This proposal seeks to investigate the nature of the spectral gap for hyperbolic surfaces and unitary representations of fundamental groups of surfaces. In the former case, the spectral gap occurs in the spectrum of the Laplace-Beltrami operator on the surface, and in the latter, it occurs in the spectrum of a Hecke operator attached to the representation. The two main motifs of the proposal are ubiquity and optimality. Is the spectral gap ubiquitous? Does it exist for random surfaces and random representations? Is it easy to construct surfaces with a large spectral gap? In what cases can one prove that the spectral gap is close to optimal? The sharpest and most ambitious questions discussed in this proposal combine these two aspects and ask whether objects with (almost) optimal spectral gap appear with high frequency.

The successful applicant will be expected to fit into one of two sub-teams of the project. One of the sub-teams will be working in `Analysis, Dynamics, and Spectral Geometry’. The other sub-team will be working on `Integration on Representation Varieties’.

The post comes with a generous allocation of travel money and opportunities to speak at international workshops that form part of the project.

Responsibilities :

  • To publish high quality outputs, including papers for submission to peer reviewed journals under the direction of the Principal Investigator.
  • To assist with the development of research objectives.
  • To conduct individual and collaborative research projects under the direction of the Principal Investigator.
  • To work with the Principal Investigator and other colleagues in the research group, as appropriate, to identify areas for research.
  • To deal with problems that may affect the achievement of research objectives and deadlines by discussing with the Principal Investigator and offering creative or innovative solutions.
  • To contribute to fostering a collegial and respectful working environment which is inclusive and welcoming and where everyone is treated fairly with dignity and respect.
  • Engage in a weekly seminar with the other team-members of the project.
  • Travel to international conferences to forge collaborations and disseminate research results.

This post is fixed term for 36 months. The post is funded by the European Research Council and the project has allocated funding for this time period only.

The post-holder is employed to work on a research project which will be led by another colleague. Whilst this means that the post-holder will not be carrying out independent research in his/her own right, the expectation is that they will contribute to the advancement of the project, through the development of their own research ideas.

Successful applicants will, ideally, be in post by 1st October 2021. 

How to Apply

For informal enquiries please contact Michael Magee by email at michael.r.magee@durham.ac.uk..  All enquiries will be treated in the strictest confidence. 

We prefer to receive applications online via the Durham University Vacancies Site. https://www.dur.ac.uk/jobs/. As part of the application process, you should provide details of 3 (preferably academic/research) referees and the details of your current line manager so that we may seek an employment reference.

Applications are particularly welcome from women and black and minority ethnic candidates, who are under-represented in academic posts in the University 

What to Submit

All applicants are asked to submit:

  • A CV and covering letter which details your experience, strengths and potential in the requirements set out above;

  • A research statement of at most 2 pages.

Next Steps

The assessment for the post will include a shortlisting process followed by Zoom interviews. Shortlisted candidates will be invited for interview and assessment in January 2021.

The Requirements



  • A PhD (or be close to submission) in Pure Mathematics or a related subject.


  • Experience in conducting high quality academic research.
  • Demonstrable ability to write material of a quality commensurate with publication in highly-ranked journals.
  • Demonstrable ability to present research results at seminars or conferences.
  • Evidence of quality research relating to one of the following areas (broadly interpreted):
  • Spectral geometry (theory of the Laplacian on manifolds or graphs)
  • The thermodynamical formalism in dynamical systems
  • Free probability theory (non-commutative probability)
  • Theory of moduli spaces of surfaces (e.g. Teichmuller theory)
  • Invariant theory of classical and symmetric groups
  • Any other research area that may be relevant to the research program


  • Demonstrable ability to work cooperatively as part of a team, including participating in research meetings.
  • Ability to work independently on own initiative and to strict deadlines.
  • Excellent interpersonal and communication skills.



  • Strong publication record in peer-reviewed journals, commensurate with stage of career.
  • A track record of presenting research at conferences, symposia, or meetings, commensurate with stage of career.
  • Demonstrable ability to develop research proposals and designs in collaboration with other academics.


  • Demonstrable ability to plan and manage independent research.

DBS Requirement: Not Applicable.