Pierre Deligne

Pierre Deligne, March 2005

Pierre René Deligne (born October 3, 1944 in Etterbeek , Brussels-Capital Region ) is a Belgian mathematician . He became famous for his complete proof of the Weil conjectures .

Life

As a high school student (where a mathematics teacher gave him Nicolas Bourbaki's set theory to read at the age of 14), Deligne attended mathematics courses at the Université Libre de Bruxelles with Jacques Tits, among others, when he was sixteen . He then went to the Université Libre de Bruxelles, but spent a large part of his four-year studies in Paris, where, following the advice of Tits, he attended the seminar of Alexander Grothendieck at the Institut des Hautes Études Scientifiques (IHES) and lectured at the Collège de France visited by Jean-Pierre Serre . He returned to Brussels for each of the exams and, after completing his studies, did his military service near Bonn in 1966 (he also attended the mathematical workshop in Bonn, but otherwise had little time to do mathematics). Then he was back at IHES at Grothendieck, who used him to work out his seminar lectures from previous years. In 1968 he received his doctorate in Brussels with Grothendieck (Théorème de Lefschetz et critères de dégénérescence de suites spectrales). He stayed at IHES and became a professor and permanent member there in 1970. In addition to Grothendieck, he also worked with Serre (on L-adic representation of module forms and functional equations of L-functions ) and with David Mumford . After being visiting professor at the Institute for Advanced Study several times (1972/73, 1976/77, 1981/2), he was a permanent member there from 1984. In 2008 he retired .

During his time at IHES, he also proved the Weil conjectures (especially the analog of the Riemann conjecture for algebraic varieties over finite fields) and the proof of the Ramanujan-Petersson conjecture from the theory of modular forms, which he based on the Weil conjectures led back. Essential for the proof of the Riemann conjecture in the Weil conjectures was the preoccupation with modular forms, to which he was led by the lectures of Jean-Pierre Serre, who also gave him his first lecture in 1969 in the Séminaire Nicolas Bourbaki on the theory of Gorō Shimura suggested. As part of the Grothendieck research program, he worked on questions of the Hodge theory (see English ) ( Mixed Hodge Theory ), category theory and the theory of motives (the concept of mixed motives comes from him). Later he also dealt with the monodromy of linear differential equations, the representation theory of finite groups, Grassmann varieties and deformation quantization. In 1980 he gave a proof (Weil II) of an even more general version of the Riemann Hypothesis for varieties over finite fields.

With Alexander Beilinson , Joseph Bernstein , Ofer Gabber , he introduced perverse sheaves in the early 1980s and proved the decomposition theorem and other properties for special perverse sheaves. Proven by the early 1980s, these theorems were seen as a major advance with many applications.

In 1974 he gave a plenary lecture at the International Congress of Mathematicians (ICM) in Vancouver (Poids dans la cohomologie des varietes algebriques), and in 1970 he was invited speaker at the ICM in Nice (Theory de Hodges I) .

He has been married to Elena Alexeeva (daughter of the Russian mathematician VM Alexeev ) since 1980 and has two children. He was in the early 1970s for the first time in Moscow (to a banquet for the 80th birthday Vinogradov ), there attended the conference from Israel Gelfand and Yuri Manin and returned there regularly back. After the fall of the Wall he supported the Independent University of Moscow (a mathematics competition is named after him there).

Awards

Deligne has received numerous awards for his work. In 1974 he received the Francois Deruyts Prize of the Belgian Academy of Sciences and in the same year the Poincaré Medal of the French Academy of Sciences named after Henri Poincaré . He also received the Fields Medal in 1978 , the Crafoord Prize in 1988 (with Grothendieck), the Balzan Prize in 2004 and the Wolf Prize in 2008 (together with Phillip Griffiths and David Mumford ). He is a member of the French Academy of Sciences, the Accademia dei Lincei, the Royal Belgian Academy of Sciences, the Royal Swedish Academy of Sciences , the National Academy of Sciences , the American Philosophical Society and the American Academy of Arts and Sciences . In 2004 he became an honorary member of the London Mathematical Society for his monumental contributions to algebraic geometry . In 2013 he received the Abel Prize .

literature

Marian Schmidt: Hommes de Science. 28 portraits. Hermann, Paris 1990, ISBN 2-7056-6124-7 (interview).

Fonts (selection)

with David Mumford : The irreducibility of the space of curves of given genus. In: Institut des Hautes Etudes Scientifiques. Publications Mathématiques. Volume 36, 1969, pp. 75-109, ( online ).
Equations différentielles à points singuliers réguliers (= Lecture Notes in Mathematics . 163). Springer, Berlin et al. 1970, ISBN 3-540-05190-2 .
Théorie de Hodge.
- I in: Actes du Congrès International des Mathématiciens 1970. (1-10 September 1970, Nice, France). Volume 1: Documents, Médailles fields, Conférences générales (G), Logique (A), Algèbre (B). Gauthier-Villars, Paris 1971, pp. 425-430, ( online );
- II in: Institut des Hautes Etudes Scientifiques. Publications Mathématiques. Volume 40, 1971, pp. 5-57, ( online );
- III in: Institut des Hautes Etudes Scientifiques. Publications Mathématiques. Volume 44, 1974, pp. 5-77, ( online ).
Les immeubles des groupes de tresses généralisés. In: Inventiones Mathematicae . Volume 17, No. 4, 1972, pp. 273-302 .
with Michael Rapoport : Les schémas de modules de courbes elliptiques. In: Pierre Deligne, Willem Kuyk (Ed.): Modular functions of one variable II. Proceedings International Summer School, University of Antwerp, RUCA, July 17 - August 3, 1972 (= Lecture Notes in Mathematics. 349). ISBN 3-540-06558-X , pp. 143-316.
La conjecture de Weil.
- I in: Institut des Hautes Etudes Scientifiques. Publications Mathématiques. Volume 43, 1974, pp. 273-307, ( online );
- II in: Institut des Hautes Etudes Scientifiques. Publications Mathématiques. Volume 52, 1980, pp. 137-252, ( online ).
with Phillip Griffiths , John Morgan , Dennis Sullivan : Real homotopy theory of Kähler manifolds. In: Inventiones Mathematicae. Volume 29, No. 3, 1975, pp. 245-274 .
with George Lusztig : Representations of reductive groups over finite fields. In: Annals of Mathematics . Series 2, Vol. 103, No. 1, 1976, pp. 103-161, doi : 10.2307 / 1971021 .
with Alexander Beilinson , Joseph Bernstein : Faisceaux pervers. In: Analyze et topologie sur les espaces singuliers. CIRM, 6-10 July 1981 (= Astérisque. 100). Volume 1. Société Mathématique de France, Paris 1982, pp. 5-171.
Le groupe fondamental de la droite projective moins trois points. In: Yasutaka Ihara , Kenneth Ribet , Jean-Pierre Serre (eds.): Galois groups over . Proceedings of a Workshop held March 23-27, 1987 ${\ displaystyle \ mathbb {Q}}$ (= Mathematical Sciences Research Institute Publications. 16). Springer, New York NY 1989, pp. 79-297, ( digitized ).
Catégories tannakiennes. In: Pierre Cartier , Luc Illusie , Nicholas M. Katz , Gérard Laumon , Yuri I. Manin , Kenneth A. Ribet (eds.): The Grothendieck Festschrift. A Collection of Articles Written in Honor of the 60th Birthday of Alexander Grothendieck. Volume 2. (= Progress in Mathematics. 87). Birkhäuser, Boston MA et al. 1990, ISBN 0-8176-3428-2 , pp. 111-195.
Quelques idées maîtresses de l'œuvre de A. Grothendieck. In: Michèle Audin (ed.): Matériaux pour l'histoire des mathématiques au XX ^e siècle. Actes du colloque à la mémoire de Jean Dieudonné (Nice 1996) (= Collection SM F. Séminaires et congrès. 3). Société Mathématique de France, Paris 1998, ISBN 2-85629-065-5 , pp. 11-19.

Web links

Commons : Pierre Deligne - Collection of images, videos and audio files

Individual evidence

^ Interview with Robert MacPherson, Simons Foundation, 2012
^ Mark Andrea A. de Cataldo , Luca Migliorini : The Decomposition theorem, perverse sheaves and the topology of algebraic maps. In: Bulletin of the American Mathematical Society . Volume 46, No. 4, 2009, pp. 535-633, ( online ).

personal data
SURNAME	Deligne, Pierre
ALTERNATIVE NAMES	Deligne, Pierre René (full name)
BRIEF DESCRIPTION	Belgian mathematician
DATE OF BIRTH	October 3, 1944
PLACE OF BIRTH	Etterbeek , Brussels-Capital Region

[1] Interview with Robert MacPherson, Simons Foundation, 2012

[2] Mark Andrea A. de Cataldo , Luca Migliorini : The Decomposition theorem, perverse sheaves and the topology of algebraic maps. In: Bulletin of the American Mathematical Society . Volume 46, No. 4, 2009, pp. 535-633, ( online ).