Davenport’s problem with a difference

The School of Mathematical Sciences of Queen Mary University of London invite applications for a PhD project commencing either in September 2016 (funded students) or at any point in the academic year (self-funded students).

Consider two polynomials with rational coefficients which which have the same ranges modulo p for all but finitely many primes p. Davenport asked whether such polynomials must be tied by a linear change of variables. There is a large body of work on this problem, most notably by Fried and Muller, showing that, under additional hypothesis, the answer is affirmative. In general, the answer is far from straightforward.

The goal of this project is to use the recent work of Dr Tomasic in difference algebra and geometry to extend these considerations to the study of difference polynomials over algebraic closures of finite fields equipped with powers of the Frobenius automorphism. The project is aimed at a student with interests in algebraic geometry, number theory and interactions with model theory and logic.

This project will be supervised by Dr Ivan Tomasic.

Further details can be found in the project abstract: http://www.maths.qmul.ac.uk/sites/default/files/phd%20projects%202015/G&A/phdproj4.pdf

The application procedure is described on the School website. For further enquiries please contact Dr Ivan Tomašić ([Email Address Removed]).

This project is eligible for several sources of full funding for the 2016/17 academic year, including support for 3.5 years’ study, additional funds for conference and research visits and funding for relevant IT needs. Applicants interested in the full funding will have to participate in a highly competitive selection process. The best candidates will be eligible to receive a prestigious Ian Macdonald Postgraduate Award of £1000, for which you will be considered alongside your application. The application deadline for full funding is January 31st 2016.

There is also 50% funding scheme available for students who are able to find the matching 50 % of the cost of their studies. Competition for these half-funded slots will be less intensive, and eligible students should mention their willingness to be considered for them in their application. The application deadline for 50 % funding is January 31st 2016.

This project can be also undertaken as a self-funded project, either through your own funds or through a body external to Queen Mary University of London. Self-funded applications are accepted year-round.