Jan Denef
Encyclopedia
Belgium
Belgium , officially the Kingdom of Belgium, is a federal state in Western Europe. It is a founding member of the European Union and hosts the EU's headquarters, and those of several other major international organisations such as NATO.Belgium is also a member of, or affiliated to, many...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
. He is Full Professor of Mathematics at the Katholieke Universiteit Leuven
Katholieke Universiteit Leuven
The Katholieke Universiteit Leuven is a Dutch-speaking university in Flanders, Belgium.It is located at the centre of the historic town of Leuven, and is a prominent part of the city, home to the university since 1425...
.
He is a specialist of model theory
Model theory
In mathematics, model theory is the study of mathematical structures using tools from mathematical logic....
, number theory
Number theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...
and algebraic geometry
Algebraic geometry
Algebraic geometry is a branch of mathematics which combines techniques of abstract algebra, especially commutative algebra, with the language and the problems of geometry. It occupies a central place in modern mathematics and has multiple conceptual connections with such diverse fields as complex...
. He is well known for his early work on Hilbert's tenth problem
Hilbert's tenth problem
Hilbert's tenth problem is the tenth on the list of Hilbert's problems of 1900. Its statement is as follows:Given a Diophantine equation with any number of unknown quantities and with rational integral numerical coefficients: To devise a process according to which it can be determined in a finite...
and for developing the theory of motivic integration
Motivic integration
Motivic integration is a branch of algebraic geometry which was invented by Maxim Kontsevich in 1995 and was developed by Jan Denef and François Loeser. Since its introduction it has proved to be quite useful in various branches of algebraic geometry, most notably birational geometry and...
in a series of papers with François Loeser
François Loeser
François Loeser is a French mathematician. He is Professor of Mathematics at thePierre and Marie Curie University in Paris. From 2000 to 2010 he was Professor atÉcole Normale Supérieure....
. He has also worked for a while on computational number theory.
Recently he proved a conjecture of Jean-Louis Colliot-Thélène
Jean-Louis Colliot-Thélène
Jean-Louis Colliot-Thélène is a French mathematician, born on 2 December 1947. He is a Directeur de Recherches at CNRS at the Université Paris-Sud in Orsay.He studies mainly number theory and algebraic geometry with an arithmetic flavor.-Awards:...
which generalizes the Ax-Kochen theorem.
He was an invited speaker at ICM 2002. His Hirsch-index is 24.