PhD Studentship: Topics in number theory



Deadline: 20 January 2014.

Start Date: October 2014.

Supervisory Team: Primary Supervisor: Dr Stephan Baier Email: [email protected]

The Project:

This project is for study in the Number Theory group at UEA, supervised by Shaun Stevens and/or Stephan Baier. Research in the number theory group falls into two main areas: Analytic Number Theory; and Representations of p-adic groups and Arithmetic.

In analytic number theory, there is a special focus on on questions relating to currently active research areas such as Manin’s conjecture on the density of rational points on Del Pezzo surfaces, small gaps between primes and subconvexity bounds for automorphic L-functions. Other topics, including large sieve type inequalities and applications, and exponential sums with coefficients of L-functions, are also studied.

In the representation theory of p-adic groups, research concentrates on questions in the local Langlands correspondence, which gives (often still conjectural) correspondences between representations of galois groups of extensions of p-adic fields and irreducible representations of p-adic matrix groups. The problems which would be examined could include: understanding the irreducible representations (and the category of all representations) of p-adic matrix groups in a very explicit way; looking at invariants of these representations, such as L-functions; exploring congruences between these representations; and exploring implications via the Langlands correspondence to arithmetic.

In all cases, the specific topic to be studied will depend very much on the interests and background of the applicant. More details about these topics can be found at www.uea.ac.uk/mathematics/research-degrees/number-theory.

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Entry Requirements:  First degree (2.1) in Mathematics.

Funding:

Due to funding restrictions funding for PhD studentships from EPSRC is available to successful candidates who meet the UK Research Council eligibility criteria including the 3-year UK residency requirements. These requirements are detailed in the EPSRC eligibility guide which can be found at http://www.epsrc.ac.uk/skills/students/help/Pages/eligibility.aspx.

In most cases UK and EU nationals who have been ordinarily resident in the UK for 3 years prior to the start of the course are eligible for a full-award.  Other EU nationals may qualify for a fees only award.  All candidates should check to confirm their eligibility for funding.

Making Your Application:

Please apply via the University’s online application system.

NB: Applications are processed as soon as they are received, so early application is encouraged.

To discuss the application process or particular projects, please contact the: Admissions Office, email: [email protected] or telephone +44 (0)1603 591709. 

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