Logic List Mailing Archive

PhD student position in model theory, Norwich (England)

Model theory and quasiminimality for analytic functions (KIRBYJ_U21SCIEPO)
University of East Anglia, School of Mathematics

https://www.findaphd.com/phds/project/model-theory-and-quasiminimality-for-analytic-functions-kirbyj-u21sciepo/?p127164

Dr J Kirby, Dr Asaf Karagila

About the Project. The project 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, Pila and others), and to Diophantine geometry, for example the 
formulation of the Zilber-Pink conjecture, and recent progress on it. On 
the model-theoretic side, there have been new developments in abstract 
stability theory developing the tools such as quasiminimality, used 
particularly for studying the complex exponential. Dr Kirby is at the 
forefront of several of these developments and currently has an 
EPSRC-funded project in this area.

In this project, you will take some functions arising in complex or p-adic 
analysis, such as correspondences between elliptic curves or the Iwasawa 
logarithm, and attempt to show that their logical theory is quasiminimal: 
that every definable set is either countable or the complement of a 
countable set. When this can be proved, systems of equations involving 
this function will have solutions which can be understood geometrically, 
in a similar way to algebraic geometry, which applies to polynomial 
functions.

Methods likely to be useful arise from model theory, topology, algebraic 
geometry, and real, complex and p-adic analysis. Candidates should have 
knowledge of at least one or two of these areas and are advised to contact 
Dr Kirby to discuss their application.

For more information on the supervisor for this project, please go here 
https://people.uea.ac.uk/jonathan_kirby

This is a PhD programme. The start date is 1st October 2021. The mode of 
study is full time. This 3.5 year PhD studentship is funded by an EPSRC 
Doctoral Training Partnership. NB. 3.5 year studentships have a 
(non-funded) 6 month 'registration only' period

Entry requirements: 1st class degree or equivalent in Mathematics.

Funding Notes. Successful candidates who meet UKRI's eligibility criteria 
will be awarded an EPSRC funded studentship covering fees, stipend 
(£15,285 pa, 2020-21), and research funding for 3.5 years. International 
applicants (EU/non-EU) are eligible for fully-funded EPSRC studentships. 
The eligibility requirements are detailed in the UKRI Training Grant 
Guidance.

Applicants to this project will also be considered for a 3 year UEA funded 
studentship covering stipend (£15,285 pa, 2020-21), tuition fees (Home 
only) and research costs. International applicants (EU/non-EU) are 
eligible for UEA funded studentships but they are required to fund the 
difference between Home and International tuition fees.
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