PhD Studentship: Model Theory of Analytic Functions (KIRBYJ_U18SCI)

University of East Anglia - Mathematics

Start Date: October 2018

Supervisor: Dr Jonathan Kirby

Project description:

This PhD is based on the recent exciting developments in the application of model theory, a branch of mathematical logic, to analytic functions such as exponentiation. These include Wilkie’s proof that the real exponential function has a tame (so-called o-minimal) geometry, and the programme started by Zilber studying the complex exponential function by algebraic/model-theoretic means. There are also exciting relations to number theory, particularly transcendence theory (for example proofs of functional transcendence theorems by Kirby, Kowalski, and other model theorists), and to Diophantine geometry, for example the formulation of the Zilber-Pink conjecture, and recent progress on it by Pila and others. On the model-theoretic side, there have been new developments in abstract stability theory developing the tools used particularly for studying the complex exponential. Dr Kirby is at the forefront of several of these developments.

The precise development of the project will take the student’s background into account. Applicants should have some knowledge of at least one of mathematical logic, model theory, algebraic varieties, complex analysis, or algebraic number theory. Please contact Dr Kirby directly to discuss your application.

Interviews will be held w/c 22 January 2018.

Person specification: Acceptable first degree: Mathematics.

Minimum entry requirement: 1st class degree.

Funding notes:

This PhD project is in a Faculty of Science competition for funded studentships. These studentships are funded for 3 years and comprise home/EU fees, an annual stipend of £14,553, and £1,000 per annum to support research training. Overseas applicants may apply but they are required to fund the difference between home/EU and overseas tuition fees (in 2017/18 the difference is £13,805 for the Schools of CHE, PHA, & MTH (Engineering) and £10,605 for CMP & MTH, but fees are subject to an annual increase).

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