PhD Studentship: Analytic Number Theory over Function Fields

University of Exeter - College of Engineering, Mathematics and Physical Sciences

The Department of Mathematics at the University of Exeter in the College of Engineering, Mathematics and Physical Sciences, is inviting applications for a Leverhulme fully-funded PhD studentship to commence in September 2018 or as soon as possible thereafter under the supervision of Dr Julio Andrade under the Leverhume research grant entitled “Moments of L-functions in Function Fields and Random Matrix Theory”.  For eligible students the studentship will cover UK/EU tuition fees plus an annual tax-free stipend of at least £14,777 for 3.5 years full-time, or pro rata for part-time study.  The student would be based in Exeter in the department of mathematics at the College of Engineering, Mathematics and Physical Sciences at the Streatham Campus in Exeter.

Location: Mathematics, Streatham Campus, CEMPS, Exeter

Academic Supervisors:
Dr Julio Andrade, University of Exeter
Professor Nigel Byott, University of Exeter

Project Description:
In the past decade there has been an explosion of activity involving function field analogues of important problems in number theory. It is in this scope that this project is inserted. The student will study classical analytic techniques and methods from analytic number theory and employ these tools to solve several classical problems from number theory in the function field context. Specifically, the main subject of study will be the Euler-Hadamard hybrid formula and its relationship with the random matrix theory. Other topics include the study of distribution of zeros of L-functions such as one-level density and pair correlation. For the final parts of the project, the student will focus on investigating several problems related to arithmetic functions for the polynomial ring over a finite field.

This award provides annual funding to cover UK/EU tuition fees and a tax-free stipend.  For students who pay UK/EU tuition fees the award will cover the tuition fees in full, plus at least £14,777 per year tax-free stipend. 

The studentship will be awarded on the basis of merit for 3.5 years of full-time study to commence in September 2018.   

Entry requirements:
Applicants for this studentship must have obtained, or be about to obtain, a First or Upper Second Class UK Honours degree, or the equivalent qualifications gained outside the UK, in an appropriate area of science or technology. It is desirable (but not essential) to have some research experience in mathematics and a master’s degree in Mathematics and/or allied fields. 
If English is not your first language you will need to have achieved at least 6.0in IELTS and no less than 6.0 in any section by the start of the project.  Alternative tests may be acceptable (see

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South West England