Daniel Bennequin (3 January 1952) is a French mathematician, known for the
Thurston–Bennequin number In the mathematical theory of knots, the Thurston–Bennequin number, or Bennequin number, of a front diagram of a Legendrian knot is defined as the writhe of the diagram minus the number of right cusps. It is named after William Thurston and Dan ...
(sometimes called the Bennequin number) introduced in his doctoral dissertation.
Education and career
Bennequin completed his secondary education at
Lycée Condorcet
The Lycée Condorcet () is a school founded in 1803 in Paris, France, located at 8, rue du Havre, in the city's 9th arrondissement. It is one of the four oldest high schools in Paris and also one of the most prestigious. Since its inception, var ...
and then graduated from the
École normale supérieure
École may refer to:
* an elementary school in the French educational stages normally followed by secondary education establishments (collège and lycée)
* École (river), a tributary of the Seine flowing in région Île-de-France
* École, Savoi ...
. He received his
habilitation
Habilitation is the highest university degree, or the procedure by which it is achieved, in many European countries. The candidate fulfills a university's set criteria of excellence in research, teaching and further education, usually including a ...
(Doctoral d'Etat) in 1982 from the
University of Paris VII
A university () is an institution of higher (or tertiary) education and research which awards academic degrees in several academic disciplines. Universities typically offer both undergraduate and postgraduate programs. In the United States, t ...
under
Alain Chenciner with thesis ''Entrelacements et équations de Pfaff''. He was a professor at the
University of Strasbourg
The University of Strasbourg (french: Université de Strasbourg, Unistra) is a public research university located in Strasbourg, Alsace, France, with over 52,000 students and 3,300 researchers.
The French university traces its history to the ea ...
before becoming a professor at the University of Paris VII (Institut Mathématique de Jussieu).
Bennequin's dissertation was a major contribution to
contact geometry
In mathematics, contact geometry is the study of a geometric structure on smooth manifolds given by a hyperplane distribution (differential geometry), distribution in the tangent bundle satisfying a condition called 'complete non-integrability'. ...
, in which he gave the first example of an exotic contact structure embedded in Euclidean 3-space. On the basis of their work in the 1980s Bennequin and
Yakov Eliashberg
Yakov Matveevich Eliashberg (also Yasha Eliashberg; russian: link=no, Яков Матвеевич Ðлиашберг; born 11 December 1946) is an American mathematician who was born in Leningrad, USSR.
Education and career
Eliashberg receiv ...
might be considered the founders of contact topology. Bennequin also works on
motion planning
Motion planning, also path planning (also known as the navigation problem or the piano mover's problem) is a computational problem to find a sequence of valid configurations that moves the object from the source to destination. The term is used ...
. He was a member of
Bourbaki.
Selected publications
* ''L'instanton gordien, d'après P. B. Kronheimer et T. S. Mrowka'', Séminaire Bourbaki Nr. 770, 1992/93
numdam* ''Monopôles de Seiberg-Witten et conjecture de Thom, d'après Kronheimer, Mrowka et Witten'', Séminaire Bourbaki Nr. 807, 1995/96
numdam* ''Caustique mystique, d'après Arnold et. al.'', Séminaire Bourbaki, Nr. 634, 1984/85
numdam* ''Problèmes elliptiques, surfaces de Riemann et structures symplectiques, d'après M. Gromov'', Séminaire Bourbaki, Nr. 657, 1985/86
numdam* ''Topologie symplectique, convexité holomorphe et structures de contact, d'après Y. Eliashberg, D. Mc Duff et al'', Séminaire Bourbaki, Nr. 725, 1989/90
numdam* ''Dualités de champs et de cordes, d’après t'Hooft, Polyakov, Witten et al.'', Séminaire Bourbaki, Nr. 899, 2001/02
numdam* ''Les Bords des revêtements ramifiés des surfaces'', ENS 1977
References
External links
Conference in honor of Bennequin, 2012
{{DEFAULTSORT:Bennequin, Daniel
1952 births
Living people
20th-century French mathematicians
21st-century French mathematicians
Academic staff of the University of Strasbourg
Academic staff of the University of Paris
École Normale Supérieure alumni
Nicolas Bourbaki