Projects per year
Personal profile
Key Research Interests
My research is primarily in Model Theory and its connections with number theory and analytic functions.
A major theme is the complex exponential function, which is used to describe both exponential growth and decay and sinusoidal wave patterns. Despite it being one of the most central of mathematical tools, there are still basic questions about the theory of the exponential function which are completely open.
Complex numbers which can be described as solutions to a polynomial equation, like the square root of 2, are called algebraic. If they are irrational, this description does not pin them down exactly, for example 2 has both a positive and negative square root. The paper The algebraic numbers definable in various exponential fields with Macintyre and Onshuus, explains when we can use exponentiation to pick out exactly one solution.
In A geometric approach to some systems of exponential equations, Aslanyan, Mantova and I gave new situations where one can find complex solutions to equations. The general conjecture, called ExponentialAlgebraic Closedness, is still open.
This ExponentialAlgebraic Closedness is built into Zilber's exponential field, and I have done much work on the theory of that structure, such as in Pseudoexponentialmapsvariantsandquasiminimality with Bays, and its connections with the complex exponential such as in Blurredcomplexexponentiation.
Connections with number theory include A Schanuelpropertyforexponentiallytranscendentalpowers with Bays and Wilkie on (functional) transcendence and with diophantine geometry such as Exponentiallyclosedfieldsandtheconjectureonintersectionswith tori with Zilber.
I am also interested in other analytic functions, for example the work Differentialexistentialclosednessforthejfunction with Aslanyan and Eterovic, and via ominimality with Jones and Servi in Local interdefinability of Weierstrass elliptic functions.
Model Theory is an approach to doing mathematics which stems from the idea of formalising, or "mathematising" the language we use when doing mathematics. It has its own collection of techniques which are related to ideas from other areas of mathematics including combinatorics (often infinite, set theoretic combinatorics), geometry, algebra, and topology.
Within Model Theory, I am particularly interested in extending the techniques to applications slightly outside the usual scope of "classical first order" model theory, such as to positive logic as in Existentiallyclosedexponentialfields with Haykazyan and to the very general "formalismfree" context of abstract elementary categories as in Quasiminimalstructuresandexcellence with Bays, Hart, Hyttinen and Kesälä, and the work of my former PhD student Mark Kamsma.
Follow this link for details of current PhD opportunities in Mathematics. But feel free to email me to discuss projects outside these areas and alternative sources of funding.
See my personal webpage for more information about my research and teaching.
Career
Reader and Associate Professor in Mathematics, UEA, 2019 
Senior Lecturer in Mathematics, UEA, 2014  2019
Lecturer in Pure Mathematics, UEA, 2009  2014
EPSRC Postdoctoral Fellow, University of Oxford, 2007  2009
Research Assistant Professor, University of Illinois at Chicago, 2006  2007
DPhil, University of Oxford, 2002  2006
MSc in Mathematical Logic, University of Manchester, 2001  2002
MA and Certificate of Advanced Studies in Mathematics, University of Cambridge, 1997  2001
Teaching Interests
I have taught a variety of subjects for undergraduates including Model Theory, Mathematical Logic, Real and Complex Analysis, Calculus, Combinatorics, and Computability. I have also taught Category Theory to PhD students via the MAGIC consortium of universities.
My book An Invitation to Model Theory is suitable for students at the beginning Masters or PhD level, and can also be read by researchers in other fields as an overview of the basic concepts of Model Theory.
Key Responsibilities
 Deputy Director of Teaching in MTH 2022  2023
 LMS Departmental Representative for UEA 2013 
 Senior Advisor in MTH 2014  2022
 Disability Liaison Officer for MTH 2014  2022
 Chairman of MTH/ENG Extenuating Circumstances Panel 2014  2021
I have also been the Student Partnership Officer for MTH, the Director of Equality and Diversity in MTH, and the MAGIC coordinator.
Collaborations and top research areas from the last five years
Projects
 7 Finished

Some model theory of elliptic functions
London Mathematical Society (The)
16/10/23 → 20/10/23
Project: Research

The Galois Theory of Exponential Fields
London Mathematical Society (The)
13/06/22 → 22/07/22
Project: Training

Exponentially Algebraically closed fields.
Engineering and Physical Sciences Research Council
1/09/19 → 31/08/22
Project: Research


Model Theory Around the JInvariant.
Engineering and Physical Sciences Research Council
24/02/14 → 23/02/16
Project: Research

Quasiminimality of complex powers
Gallinaro, F. & Kirby, J., 15 Jun 2024, (Accepted/In press) In: Forum of Mathematics, Sigma.Research output: Contribution to journal › Article › peerreview
Open AccessFile4 Downloads (Pure) 
Up with categories, down with sets; Out with categories, in with sets!
Kirby, J., Jun 2024, In: Philosophia Mathematica. 32, 2, p. 216–227 12 p.Research output: Contribution to journal › Article › peerreview
Open AccessFile4 Downloads (Pure) 
A closure operator respecting the modular jfunction
Aslanyan, V., Eterović, S. & Kirby, J., Mar 2023, In: Israel Journal of Mathematics. 253, p. 321–357 37 p.Research output: Contribution to journal › Article › peerreview
Open AccessFile6 Downloads (Pure) 
A geometric approach to some systems of exponential equations
Aslanyan, V., Kirby, J. & Mantova, V., Mar 2023, In: International Mathematics Research Notices. 2023, 5, p. 4046–4081 36 p.Research output: Contribution to journal › Article › peerreview
Open AccessFile2 Citations (Scopus)19 Downloads (Pure) 
Independence relations for exponential fields
Aslanyan, V., Henderson, R., Kamsma, M. & Kirby, J., Aug 2023, In: Annals of Pure and Applied Logic. 174, 8, 103288.Research output: Contribution to journal › Article › peerreview
Open AccessFile12 Downloads (Pure)
Activities

British Logic Colloquium (External organisation)
Jonathan Kirby (President)
2023 → …Activity: Membership › Network, Working Group or Professional Association

Bulletin of the London Mathematical Society (Journal)
Jonathan Kirby (Advisory Board Member)
2020 → …Activity: Editorial work › Publication editorial role

Journal of the London Mathematical SocietySecond Series (Journal)
Jonathan Kirby (Advisory Board Member)
2020 → …Activity: Editorial work › Publication editorial role