Matthias Kreck

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Matthias Kreck in Oberwolfach (2000)

Matthias Kreck (born July 22, 1947 in Dillenburg ) is a German mathematician who deals with algebraic topology and differential topology . From October 2006 to September 2011 he was director of the Hausdorff Research Institute for Mathematics at the University of Bonn , and has been a professor at the Mathematical Institute there since then.

life and work

Kreck grew up as the son of theologian Walter Kreck in Herborn and studied mathematics and physics as well as business administration at the universities of Bonn, Berlin and Regensburg from 1966 to 1970 . In 1970 he took his diploma in mathematics in Bonn and in 1972 he did his doctorate there under Friedrich Hirzebruch (An invariant for stable parallelized manifolds). From 1972 to 1976 he studied Protestant theology in Bonn, while at the same time he was Hirzebruch's assistant from 1970 to 1976. In 1977 he received his habilitation in mathematics on the subject of Bordism groups of diffeomorphisms .

In 1976 he became a professor at the University of Wuppertal and in 1978 at the University of Mainz . From 1994 to 2002 he was director of the Mathematical Research Institute in Oberwolfach . In 1999 he became a professor at the University of Heidelberg and from 2007 to 2011 he was director of the Hausdorff Research Institute for Mathematics at the University of Bonn, which he established. He was visiting professor at the Max Planck Institute for Mathematics in Bonn from 1981/82 and 1989 to 1992 and visiting scholar in Paris, Princeton, Berkeley, Chicago, Aarhus, Saint Petersburg, Moscow and Beijing, among others.

Kreck worked on the classification of manifolds in differential topology (e.g. with Bordism groups), 4-manifolds with exotic (differentiability) structures and the interaction of differential geometry and topology. In his habilitation in 1977 he succeeded in fully classifying closed, smooth, orientable manifolds with diffeomorphisms within the framework of the Bordism theory, a problem that René Thom , William Browder and Dennis Sullivan had already worked on. He developed his own theory of surgery, which is applicable under weaker conditions than classical theories of surgery, and which he applied to questions of differential geometry. In the 2000s he worked on examples of asymmetric topological manifolds.

From 1990 to 1998 he was co-editor of the Mathematische Annalen and 1998 to 2002 of the Archives for Mathematics. Since 2000 he has been a member of the Heidelberg Academy of Sciences .

In 2003 he received an honorary doctorate from the University of Siegen .

In 2010 he was awarded the Georg Cantor Medal ,

In 2012 he gave the Gauss lecture .

His doctoral students include Peter Teichner , Director at the Max Planck Institute for Mathematics in Bonn , and Stephan Stolz .

In the course of the “ plagiarism affair ”, at the end of February 2011 he initiated a “Declaration by university professors on the standards of academic examinations” and the associated signature campaign. First signatories were u. a. Martin Carrier , Eckhard Freise , Gerhard Huisken and Werner Nahm .

In his spare time he plays the cello .

Publications

  • Differential algebraic topology- from stratifolds to exotic spheres, American Mathematical Society 2010
  • Bordism of diffeomorphisms and related topics, Springer Lecture Notes in Mathematics, Vol. 1069. 1984 (Appendix Neal Stoltzfus)
  • Exotic structures on 4-manifolds, Annual Report DMV, Vol. 88, 1986, pp. 124–145
  • Editor with Wolfgang Lück : The Novikov Conjecture - geometry and algebra, Birkhäuser 2005 (Oberwolfach Seminar)
  • Positive curvature and topology, NRW Academy of Sciences, Opladen, Westdeutscher Verlag 1994
  • Kreck, Hambleton: On the classification of topological 4-manifolds with finite fundamental group Mathematische Annalen, Vol. 280, 1988, p. 85
  • Kreck, Lück, Teichner: Counterexamples of the Kneser conjecture in dimension 4 Comm.Math.Helveticae Vol. 70, 1995, p. 423
  • Kreck: Surgery and duality. Ann. of Math. (2) 149 (1999) no. 3, 707-754.

Other publications

Individual evidence

  1. ↑ also with applications to 7-dimensional manifolds discussed in elementary particle physics (Kaluza-Klein theories). Kreck "Is the universe exotic?", Universitas 1988
  2. ↑ Kreck Bordism of diffeomorphisms , Bulletin AMS, Volume 82, 1976, pp. 759-761
  3. ^ Gabriele Dörflinger: Mathematics in the Heidelberg Academy of Sciences . 2014, p. 43
  4. ↑ University protocols for an honorary doctorate in Siegen
  5. ↑ Matthias Kreck in the Mathematics Genealogy Project (English)Template: MathGenealogyProject / Maintenance / name used
  6. ↑ Declaration by university professors on the standards of academic examinations ( Memento of March 4, 2011 in the Internet Archive ) (PDF; 876 kB)

Web links

personal data
SURNAME Kreck, Matthias
BRIEF DESCRIPTION German mathematician
DATE OF BIRTH July 22, 1947
PLACE OF BIRTH Dillenburg