Alain Connes, emeritus professor since 2017 - IHES
Alain Connes (IHES) © IHES

Alain Connes, Mathematician

Léon Motchane Chair holder since 1979
Emeritus College de France professor since 2017

After pioneering contributions on operator algebras, Alain Connes developed an ambitious programme aimed at founding a "noncommutative geometry".

Step by step, Alain Connes identified the elements of this new geometry, introducing new concepts such as cyclic cohomology, K-cycles theory, and a spectral approach to Riemannian geometry. The theory is now a well established branch of mathematics involving hundreds of researchers. It provides very interesting models for physics such as a synthetic and geometric view on the standard model of elementary particles, a conceptual framework for the quantum Hall effect. It also provides an encompassing view of discrete and continuous spaces. As a result, new connections are being made with number theory and algebraic geometry, via an avatar of the theory of motives.

The research activity of Alain Connes in 2019 focused on algebraic geometry and Segal’s Γ-rings, as well as the role of spectral realisation and Hilbertian interpretation of local contributions to the Riemann-Weil formula.

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Aimé Berthé prize of the Académie des sciences (1975)
Peccot-Vimont Prize of the Collège­ de France (1977)
"Prix Ampère de l'Électricité de France", Académie des Sciences (1980)
Fields Medal (1982)
Clay Prize (2000)
Crafoord Prize (2001)
CNRS Gold Medal (2004)
Institut de France member


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