Contact details


Telephone number: 01865 284429

Role: Fellow and Tutor; University Lecturer

Prof Koenigsmann


Before joining LMH in 2007, I was Research Fellow at the Max Planck Institute for Mathematics in Bonn for one year. Prior to that I was a Heisenberg research fellow for five years, and associate professor in Konstanz (where I got my habilitation), Freiburg, Ulm and Philadelphia. I had extended research visits in Cambridge, Paris, Rennes, Lille, Copenhagen, Heidelberg, Tel Aviv, Jerusalem, Novosibirsk, Kyoto, Campinas, Rio de Janeiro, Saskatoon, Berkeley and Princeton. I was co-founder and fellow of the Freiburg Graduate School of Mathematical Logic and Applications (2002-2008, funded by the DFG, the German Research Foundation). I co-organised conferences in Oxford, Edinburgh, Freiburg, Konstanz, Oberwolfach and Luminy. I am a regular invitee to workshops at MFO Oberwolfach, CIRM Luminy and MSRI Berkeley. I am the Invited Speaker at the International Congress of Mathematicians (ICM), taking place in Rio de Janeiro in August 2018.

Research interests

I am a member of the Mathematical Logic Group at the Mathematical Institute Oxford. My research interests are in logic, algebra and number theory. More specifically I have proved theorems on valuation theory, on model theory and on arithmetic of fields, on infinite Galois theory, on the Inverse Galois Problem, on Hilbert’s 10th Problem, on undecidability in number theory, on Grothendieck’s anabelian geometry and on profinite groups. You can watch two of my research talks in Luminy (2015) and at IHP Paris (2018).



At LMH I am tutoring all 1st and 2nd year undergraduates on algebraic topics (linear algebra, group theory, number theory etc.). In 2008 I launched the LMH Maths Seminar which brings together all mathematicians of the College (undergraduates, graduates, and tutors) once a term.

At the Mathematical Institute I regularly give lectures on Logic (Part B), Model Theory (Part C) and Valuation Theory (graduate lecture). I have also been running the Logic Seminar for many years.

I was Prelims Examiner for Paper I in 2015, 2016, and 2017.

Six students have finished their PhD under my supervision; there are currently three more in their final year.

I have taught graduate courses on Undecidability in Number Theory during summer schools in Cetraro and Oxford (both in 2012).

Select Bibliography

  •  J Koenigsmann, Decidability in local and global fields, Proceedings of the ICM, 2018
  • J Koenigsmann, Defining Z in Q, Annals of Mathematics 183(1), 2016
  • F Jahnke, J Koenigsmann, Definable Henselian valuations, Journal of Symbolic Logic 80(1), 2015
  • J Koenigsmann, Undecidability in number theory, in: Springer Lecture Notes 2111, 2014
  • W Anscombe, J Koenigsmann, (An existential 0-definition for Fq[[t]] in Fq((t))), Journal of Symbolic Logic 79(4), 2014
  • J Koenigsmann, Projective extensions of fields, Journal of the London Mathematical Society 73(3), 2006
  • J Koenigsmann, On the “Section Conjecture” in anabelian geometry, Journal für die angewandte und reine Mathematik 588, 2005
  • J Koenigsmann, The regular inverse Galois problem over non-large fields, Journal of the European Mathematical Society 6(4), 2004
  • J Koenigsmann, Solvable absolute Galois groups are metabelian, Inventiones mathematicae 144(1), 2001
  • AJ Engler, J Koenigsmann, Abelian subgroups of pro-p Galois groups, Transactions of the American Mathematical Society 350(6), 1998