EPSRC DTP PhD studentship: Some Problems in Number Theory and Random Matrix Theory

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

Main supervisor: Dr. Julio Andrade (University of Exeter)

The proposed project is in number theory, an area of pure mathematics which is concerned with prime numbers and solutions to equations. It has long been understood in the field that there are strong analogies between number theory and the geometry of curves. As a deeper understanding of this analogy could have tremendous consequences, the search for a unified approach and the reinterpretation of geometric methods has been a source of inspiration and success for number theorists.

The plan is to investigate the relation between the random matrix theory, equidistribution theorems and problems in number theory over function fields. The main idea is to investigate several arithmetic problems over function fields in the limit of a large finite field. By using recent results of Keating and Rudnick and several other authors we can relate arithmetic and number theoretical problems to zeros of L-functions and then use equidistribution results due to Katz to solve a myriad of arithmetic problems.

In this project, we are going to use the same ideas as the previous authors to attack several arithmetic problems and also we intend to investigate the general theoretical framework where the same ideas work. One of the main aims is to prove some general results where all the previous results can be seen as particular cases and this will involve the study of L-functions, equidistribution results, matrix integrals, compact groups and many other recent topics in mathematics.

The calculations involved are subtle and important, and any small progress will enormously benefit the academic career of the student. The student will have contact with very recent research and will be able to interact with members in Exeter, Bristol, Isarael and USA.

3.5 year studentship: 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.

Applicants who are classed as International for tuition fee purposes are not eligible for funding.

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South West England