Michel Demazure

The Demazure character formula, published in 1974, provides a significant extension to the Weyl character formula by analyzing specific submodules of finite-dimensional representations. This development remains one of the notable contributions from French mathematician Michel Demazure, whose career bridged the evolution of abstract algebraic geometry and the practical applications of computational vision systems.

Academic Foundations and Collaborations

Born in 1937 in Neuilly-sur-Seine, Michel Demazure pursued his education at the École Normale Supérieure and the University of Paris. During the 1960s, he engaged in intensive research under the supervision of Alexandre Grothendieck. Between 1962 and 1964, they collaborated on the Séminaire de Géométrie Algédrique du Bois Marie, which focused on group schemes. Demazure completed his doctorate in 1965 with a dissertation titled Schémas en groupes réductifs. His early career included appointments as maître de conférence at Strasbourg University, followed by a professorship at Paris-Sud in Orsay from 1966 to 1976.

Contributions to Algebraic Geometry

Demazure held a core membership in the Nicolas Bourbaki collective from approximately 1965 to 1985. In his work for SGA3, he introduced the concept of a root datum, which serves as a generalization of root systems for reductive groups and holds central importance for Langlands duality. His 1970 study on subgroups of the Cremona group is cited as the foundational work for the study of toric varieties. Although his 1974 proposal for the Demazure character formula initially relied on a flawed lemma later corrected by Victor Kac, the modules bearing his name continue to be a standard tool in representation theory.

Professional Appointments and Public Outreach

Demazure transitioned into significant administrative roles within the French scientific community. He served as the president of the Société Mathématique de France in 1988. His commitment to public science education was demonstrated during his tenure as director of the Palais de la Découverte in Paris from 1991 to 1998, and subsequently as chairman of the Cité des Sciences et de l'Industrie at La Villette until 2002. Throughout his tenure at the École Polytechnique in Palaiseau between 1976 and 1999, he oversaw research transitions toward applied mathematics.

Computer Vision and Computational Geometry

In the later stages of his career, Demazure shifted his focus toward computer vision, specifically the application of algebraic geometry to image reconstruction. He solved a long-standing problem in the field by providing a complete solution to the Kruppa–Demazure theorem. This work demonstrates that a scene containing five points viewed from two cameras with unknown positions and known focal lengths typically produces exactly ten possible geometric interpretations. This solved a problem that Austrian mathematician Erwin Kruppa had previously narrowed down to eleven possibilities.

Fast facts

• Born: 1937, Neuilly-sur-Seine
• Citizenship: France
• Doctorate: University of Paris, 1965
• Awards: Cours Peccot, 1966
• President of the Société Mathématique de France: 1988
• Languages: French, English

Questions readers ask

What is the Kruppa–Demazure theorem?

It is a result in computer vision showing that a scene of five points viewed from two cameras with unknown positions but known focal lengths yields ten possible configurations.

Was Michel Demazure part of the Bourbaki group?

Yes, he was a core member of the collective of mathematicians writing under the pseudonym Nicolas Bourbaki from approximately 1965 to 1985.

Achievements

• Held posts at École polytechnique
• Fields: mathematics, abstract algebra and algebraic geometry