Local Global Principles for Torsors Under Fundamental Groups - Mathematics - EPSRC DTP funded PhD Studentship Ref: 2889

About the award

This project is one of a number funded by the Engineering and Physical Sciences Research Council (EPSRC) Doctoral Training Partnership to commence in September 2018. This project is in direct competition with others for funding; the projects which receive the best applicants will be awarded the funding.

The studentships will provide funding for a stipend which is currently £14,553 per annum for 2017-2018. It will provide research costs and UK/EU tuition fees at Research Council UK rates for 42 months (3.5 years) for full-time students, pro rata for part-time students.

Please note that of the total number of projects within the competition, up to 15 studentships will be filled.

Prof. Mohamed Saidi
Professor Nigel Byott

Streatham Campus, Exeter

Project Description
A major problem in number theory and arithmetic geometry is the understanding of arithmetic fundamental groups as well as Galois cohomology groups of fields with arithmetic interest such as number fields or more generally finitely generated fields.

Of particular interest are some Galois cohomology groups classifying torsors under geometric fundamental groups. Local global principles in Galois cohomology are of major importance in number theory and arithmetic geometry, and usually arise as the consequence of the injectivity of some natural restrictions maps in Galois cohomology.

In a recent work I proved a local global principle for torsors under prosolvable geometric fundamental groups of algebraic curves over number field. These torsors are classified by a certain (non commutative) Galois cohomology group and the local global principle as usual reads as the injectivity of a certain restriction map in Galois cohomology.

The aim of this project is to generalise this result to other situations of arithmetic interest. For example to torsors under geometric fundamental groups of algebraic curves over finitely generated fields in characteristic zero and also curves over finitely generated fields in positive characteristics. In addition to the methods I introduced in my paper these new situations require some technical improvements and there is an opportunity to introduce and rely on new ideas and techniques. For this the successful candidate is required to become familiar with several techniques in Galois cohomology as well as the theory of arithmetic fundamental groups, and study the injectivity of certain natural restrictions maps arising in the Galois cohomology of geometric fundamental groups of curves over finitely generated fields. He or she will be required to attend some conferences, workshops, or summer schools  related to the topic of the research.

Entry Requirements
You should have or expect to achieve at least a 2:1 Honours degree, or equivalent, in Mathematics. Experience in Number theory, Galois theory, and algebraic geometry is desirable.

The majority of the studentships are available for applicants who are ordinarily resident in the UK and are classed as UK/EU for tuition fee purposes.  If you have not resided in the UK for at least 3 years prior to the start of the studentship, you are not eligible for a maintenance allowance so you would need an alternative source of funding for living costs. To be eligible for fees-only funding you must be ordinarily resident in a member state of the EU.  For information on EPSRC residency criteria click here.

Applicants who are classed as International for tuition fee purposes are NOT eligible for funding. International students interested in studying at the University of Exeter should search our funding database for alternative options.


Application deadline:10th January 2018
Value:3.5 year studentship: UK/EU tuition fees and an annual maintenance allowance at current Research Council rate. Current rate of £14,553 per year.
Duration of award:per year
Contact: Doctoral Collegepgrenquiries@exeter.ac.uk

How to apply

You will be required to upload the following documents:
•       CV
•       Letter of application outlining your academic interests, prior research experience and reasons for wishing to
        undertake the project.
•       Transcript(s) giving full details of subjects studied and grades/marks obtained.  This should be an interim
        transcript if you are still studying.
•       If you are not a national of a majority English-speaking country you will need to submit evidence of your current
        proficiency in English.  For further details of the University’s English language requirements please see

The closing date for applications is midnight (GMT) on Wednesday 10 January 2018.  Interviews will be held at the University of Exeter in late February 2018.

If you have any general enquiries about the application process please email: pgrenquiries@exeter.ac.uk.
Project-specific queries should be directed to the supervisor.

During the application process, the University may need to make certain disclosures of your personal data to third parties to be able to administer your application, carry out interviews and select candidates.  These are not limited to, but may include disclosures to:

• the selection panel and/or management board or equivalent of the relevant programme, which is likely to include staff from one or more other HEIs;
• administrative staff at one or more other HEIs participating in the relevant programme.

Such disclosures will always be kept to the minimum amount of personal data required for the specific purpose. Your sensitive personal data (relating to disability and race/ethnicity) will not be disclosed without your explicit consent.