Jan Denef (born 4 September 1951) is a Belgian mathematician. He is an Emeritus Professor of Mathematics at the

Katholieke Universiteit Leuven KU Leuven (or Katholieke Universiteit Leuven) is a Catholic research university in the city of Leuven, Belgium. It conducts teaching, research, and services in computer science, engineering, natural sciences, theology, humanities, medicine, l ...

(KU Leuven). Denef obtained his

PhD PHD or PhD may refer to: * Doctor of Philosophy (PhD), an academic qualification Entertainment * '' PhD: Phantasy Degree'', a Korean comic series * ''Piled Higher and Deeper'', a web comic * Ph.D. (band), a 1980s British group ** Ph.D. (Ph.D. albu ...

from KU Leuven in 1975 with a thesis on

Hilbert's tenth problem Hilbert's tenth problem is the tenth on the list of mathematical problems that the German mathematician David Hilbert posed in 1900. It is the challenge to provide a general algorithm which, for any given Diophantine equation (a polynomial equat ...

; his advisors were Louis Philippe Bouckaert and Willem Kuijk. He is a specialist of

model theory In mathematical logic, model theory is the study of the relationship between formal theories (a collection of sentences in a formal language expressing statements about a mathematical structure), and their models (those structures in which the s ...

, number theory and

algebraic geometry Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical ...

. He is well known for his early work on Hilbert's tenth problem and for developing the theory of motivic integration in a series of papers with

François Loeser François Loeser (born August 25, 1958) is a French mathematician. He is Professor of Mathematics at the Pierre-and-Marie-Curie University in Paris. From 2000 to 2010 he was Professor at École Normale Supérieure. Since 2015, he is a senior member ...

. He has also worked on

computational number theory In mathematics and computer science, computational number theory, also known as algorithmic number theory, is the study of computational methods for investigating and solving problems in number theory and arithmetic geometry, including algorithms ...

. Recently he proved a conjecture of

Jean-Louis Colliot-Thélène Jean-Louis Colliot-Thélène (born 2 December 1947), is a French mathematician. He is a Directeur de Recherches at CNRS at the Université Paris-Saclay in Orsay. He studies mainly number theory and arithmetic geometry. Awards *Prize of the Fren ...

which generalizes the

Ax–Kochen theorem The Ax–Kochen theorem, named for James Ax and Simon B. Kochen, states that for each positive integer ''d'' there is a finite set ''Yd'' of prime numbers, such that if ''p'' is any prime not in ''Yd'' then every homogeneous polynomial of degree '' ...

. In 2002 Denef was an Invited Speaker at the

International Congresses of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the Nevanlinna Prize (to be rename ...

in Beijing. His Hirsch-index is 24.

References

Publications

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External links

* * {{DEFAULTSORT:Denef, Jan 1951 births Living people 20th-century Belgian mathematicians 21st-century Belgian mathematicians Model theorists Academic staff of KU Leuven KU Leuven alumni