Ib Madsen

Ib Henning Madsen ( born April 12, 1942 in Copenhagen ) is a Danish mathematician who deals with topology.

Madsen attended the University of Copenhagen ( candidate 's degree in 1965 ) and received his doctorate in 1970 at Peter May at the University of Chicago. From 1971 he was assistant professor at the University of Aarhus and from 1983 professor. Since 2008 he is professor at the University of Copenhagen. He has been a visiting professor at the University of Chicago (annually 1979-1985 ), Stanford University (annually 1995-2005 ), at the Institute for Advanced Study (1986 /87) and at Princeton University.

Madsen worked among other things on the spherical space problem ( the question of finite groups acting freely on a sphere ). With C. Thomas and CTC Wall, he gave necessary and sufficient criteria for the allowed groups. Later he dealt with the topology of moduli spaces ( for example, Riemann surfaces and holomorphic bundles on such Riemann surfaces ), which he studied with the methods of algebraic topology. By Michael Weiss succeeded him ( building on the work of Ulrike Tillmann ) the proof of the Mumford conjecture ( 2004) on the algebraic structure of the cohomology of the stable moduli space of Riemann surfaces (or the stable mapping class group).

With M. Bökstedt, WC Hsiang and T. Goodwillie he led topological trace methods in the Algebraic K-theory and applied these in collaboration with his PhD student Lars Hessel Holt.

In 1978 he was invited speaker at the International Congress of Mathematicians (ICM ) in Helsinki ( Spherical Space Forms) and he held a plenary lecture at the ICM 2006 in Madrid ( moduli spaces from a topological viewpoint ). In 2004 he was invited speaker at the 4th European Congress of Mathematicians with Michael Weiss (The stable mapping class group and stable homotopy ). 1998 to 2000 he was editor of Acta Mathematica. In 1992 he received the Humboldt Research Award. He is a member of the Royal Danish Academy of Sciences (since 1978), the Swedish (since 1998) and the Norwegian Academy of Sciences (since 2000). 1996-2000 he was the Scientific Advisory Board of the Max Planck Institute for Mathematics in Bonn. In 1997, he stood before the Danish National Committee for Mathematics, which he was a member from 1995 to 2006. In 2012 he was awarded the Ostrowski Prize. He is a Fellow of the American Mathematical Society.

Madsen is married and has two children.

Writings

• With Jørgen Tornehave: From Calculus to Cohomology: de Rham Cohomology and Characteristic Classes, Cambridge University Press 1997
• With R. James Milgram: Classifying spaces for surgery and cobordism of manifolds, Princeton University Press 1979
• Smooth spherical space forms, in: Geometric applications of Homotopy Theory I, Lecture Notes in Mathematics, Bd.657, 1978 ( Proceedings, Evanston, 1977)