Ib Madsen

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Ib Madsen in Oberwolfach , 2008

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

Madsen studied at the University of Copenhagen (candidate graduation 1965) and received his doctorate in 1970 with Peter May at the University of Chicago . From 1971 he was assistant professor at Aarhus University and from 1983 professor. Since 2008 he has been a professor at the University of Copenhagen. Among other things, he was visiting professor at the University of Chicago (1979 to 1985), Stanford University (1995 to 2005), the Institute for Advanced Study (1986/87) and Princeton University .

Madsen worked, among other things, on the spherical problem of space (the question of the finite groups that operate 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 modular spaces (for example of Riemann surfaces or holomorphic bundles on such Riemann surfaces), which he investigates with methods of algebraic topology . With Michael Weiss he succeeded (building on the work of Ulrike Tillmann ) in the proof of the Mumford conjecture (2004) about the algebraic structure of the cohomology of the stable modular space of Riemann surfaces (or the stable homology of the mapping class groups ).

With M. Bökstedt, WC Hsiang and T. Goodwillie, he introduced topological trace methods into the algebraic K-theory and applied them in collaboration with his doctoral student Lars Hesselholt .

In 1978 he was invited speaker at the International Congress of Mathematicians (ICM) in Helsinki ( Spherical Space Forms ) and in 2006 he gave a plenary lecture at the ICM 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 ) and in 1992 he was invited speaker at the ECM in Paris ( The cyclotomic trace in algebraic K-theory ). From 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). From 1996 to 2000 he was on the scientific advisory board of the Max Planck Institute for Mathematics in Bonn. In 1997 he chaired the Danish National Committee for Mathematics, of which he was a member from 1995 to 2006. In 2012 he received the Ostrowski Prize . He is a fellow of the American Mathematical Society . In 2015 Madsen was elected to the Academia Europaea .

Madsen is married with two children.

Fonts

  • with R. James Milgram : Classifying spaces for surgery and cobordism of manifolds (= Annals of Mathematics Studies. 92). Princeton University Press, Princeton NJ 1979, ISBN 0-691-08225-1 .
  • Spherical space forms. In: Olli Lehto (ed.): Proceedings of the International Congress of Mathematicians, Helsinki 1978. Volume 1. Academia Scientiarum Fennica, Helsinki 1980, pp. 475-479.
  • with Marcel Bökstedt, Wu C. Hsiang : The cyclotomic trace and algebraic -theory of spaces. In: Inventiones Mathematicae . Vol. 111, No. 3, 1993, pp. 465-539 .
  • with Jørgen Tornehave: From Calculus to Cohomology. De Rham Cohomology and Characteristic Classes. Cambridge University Press, Cambridge et al. 1997, ISBN 0-521-58059-5 .
  • with Lars Hesselholt : On the -theory of local fields. In: Annals of Mathematics . Series 2, Vol. 158, No. 1, 2003, pp. 1-113, JSTOR 3597154 .
  • with Michael Weiss : The stable moduli space of Riemann surfaces: Mumford's conjecture. In: Annals of Mathematics. Series 2, Vol. 165, No. 3, 2007, pp. 843-941, JSTOR 20160047 .
  • with Søren Galatius , Ulrike Tillmann , Michael Weiss: The homotopy type of the cobordism category. In: Acta Mathematica . Vol. 202, No. 2, 2009, pp. 195-239, ( online ).

Web links

References

  1. ↑ apart from the identity, no group element leaves a point invariant
  2. ↑ Madsen, Weiss: The stable moduli space of Riemann surfaces: Mumford's conjecture. In: Annals of Mathematics. Series 2, Vol. 165, No. 3, 2007, pp. 843-941.
personal data
SURNAME Madsen, Ib
ALTERNATIVE NAMES Madsen, Ib Henning
BRIEF DESCRIPTION Danish mathematician
DATE OF BIRTH April 12, 1942
PLACE OF BIRTH Copenhagen