Jochen Koenigsmann

Jochen Koenigsmann is a German mathematician.

Koenigsmann received his doctorate in 1993 under Alexander Prestel at the University of Konstanz (half-ordered fields). After his habilitation in Konstanz, he was a private lecturer in Konstanz and at the University of Freiburg. In Freiburg from 2002 to 2008 he was a co-founder and fellow of the Graduate School for Mathematical Logic and its Applications, funded by the German Research Foundation.

Since 2007 he has been a University Lecturer at Oxford University , where he is a Tutorial Fellow at Lady Margaret Hall .

He also taught in Ulm and Philadelphia and was at the Max Planck Institute for Mathematics in Bonn. He was also visiting scholar in Cambridge, Paris, Rennes, Lille, Copenhagen, Heidelberg, Tel Aviv, Jerusalem, Novosibirsk, Kyoto, Campinas, Rio de Janeiro, Saskatoon, Berkeley and Princeton.

He deals with model theory , arithmetic of solids, number theory (especially undecidability in number theory), Galois theory (absolute Galois group, inverse Galois theory), Hilbert's 10th problem , valuation theory , profinite groups and Anabelian geometry .

In 2016 he proved that the integers are universally definable over the rational numbers . This is a step towards solving the tenth Hilbert problem over the rational numbers. He proved more precisely that there is a natural number and a polynomial such that for all : ${\displaystyle \mathbb {Z} }$ ${\displaystyle \mathbb {Q} }$ ${\displaystyle n}$ ${\displaystyle g\in \mathbb {Z} (t,x_{1},\cdots ,x_{n})}$ ${\displaystyle t\in \mathbb {Q} }$

${\displaystyle t\in \mathbb {Z} }$ if and only if ${\displaystyle \forall x_{1}\cdots \forall x_{n}\in \mathbb {Q} :\,g(t,x_{1},\cdot ,x_{n})\neq 0}$

So the complement of in is diophantine (is a Diophantine quantity) in . ${\displaystyle \mathbb {Z} }$ ${\displaystyle \mathbb {Q} }$ ${\displaystyle \mathbb {Q} }$

In his work Koenigsmann also made arguments that there is no Diophantine set in , i.e. that it cannot be defined existentially via Q. ${\displaystyle \mathbb {Z} }$ ${\displaystyle \mathbb {Q} }$

In 2018 he was invited speaker at the ICM in Rio de Janeiro . He was a scholarship holder of the German National Academic Foundation , Heisenberg scholarship holder of the DFG and received the Dornier Research Award.

Fonts (selection)

• Defining Z in Q, Annals of Mathematics, Volume 183, 2016, pp. 73-93, Arxiv
• On the 'Section Conjecture' in anabelian geometry, Journal for pure and applied mathematics (Crelles Journal), Volume 588, 2005, pp. 221-235, Arxiv
• Solvable absolute Galois groups are metabelian, Inventiones mathematicae, Volume 144, 2001, pp. 1-22
• From p-rigid elements to valuations (with a Galois characterization of p-adic fields), Journal for pure and applied mathematics, Volume 465, 1995, pp. 165-182
• Undecidability in number theory, Model theory in Algebra, Analysis and Arithmetic, Volume 2111, 2014, pp. 159-195, Arxiv
• Relatively projective groups as absolute Galois groups, Israel J. Math., Vol. 127, 2002, pp. 93-129, Arxiv
• Elementary characterization of fields by their absolute Galois groups, Sibirian Advances in Mathematics, Volume 14, 2004, pp. 1-26
• Projective extensions of fields, J. London Math. Soc., Vol. 73, 2006, pp. 639-656
• A Galois codes for valuations, 2004, ps

Web links

• Homepage
• LMH biography

Individual evidence

1. ↑ Jochen Koenigsmann in the Mathematics Genealogy Project (English)