The diploma thesis submitted by Matthias Kreck in 1970 marked the beginning of an academic career focused on the complexities of algebraic and differential topology. Born in 1947 in Dillenburg, Germany, he has spent decades advancing the classification of manifolds while navigating significant administrative roles within Europe's primary mathematical research institutions.
Academic Foundation and Early Research
Kreck attended the University of Bonn, where he studied mathematics and physics between 1966 and 1970. Under the supervision of Friedrich Hirzebruch, he completed his doctorate in 1972 with a thesis titled An invariant for stably parallelized manifolds. He continued his work under Hirzebruch as an assistant until 1976. During this period, he also undertook studies in Protestant theology in Bonn. In 1977, he achieved his habilitation with a work focused on the bordism groups of diffeomorphisms.
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His teaching career began with a professorship at the University of Wuppertal in 1976. He moved to the University of Mainz in 1978 and joined the faculty at the University of Heidelberg in 1999. He has held visiting positions at the Max Planck Institute for Mathematics in Bonn and conducted research in international cities including Princeton, Berkeley, Paris, and Moscow. From 1994 to 2002, he served as director of the Oberwolfach Research Institute for Mathematics, and he later acted as the founding director of the Hausdorff Research Institute for Mathematics in Bonn from 2007 until October 2011.
Contributions to Differential Topology
Kreck contributed to the classification of manifolds by developing a modified theory of surgery that functions under conditions weaker than those required by classical methods. In his 1977 habilitation, he classified closed smooth manifolds with diffeomorphisms up to bordism, addressing problems previously examined by mathematicians such as René Thom, William Browder, and Dennis Sullivan. His research also covers exotic differentiable structures on 4-manifolds. During the 2000s, he identified examples of asymmetric topological manifolds, including the first such instance with a trivial fundamental group.
Professional Recognition and Advocacy
The German Mathematical Society awarded him the Cantor Medal in 2010 and a Gauss Lectureship in 2012. He received an honorary doctorate from the University of Siegen in 2003 and has been a member of the Heidelberg Academy of Sciences since 2000. In 2023, he was elected as a corresponding member of the Göttingen Academy of Sciences and Humanities. Beyond his research, he took a public stance on academic integrity in 2011 by initiating a declaration on academic standards following the Guttenberg plagiarism scandal.
Fast facts
- Born: 1947, Dillenburg
- Doctoral advisor: Friedrich Hirzebruch
- Cantor Medal recipient: 2010
- Member: Heidelberg Academy of Sciences
- Primary research field: Differential topology
- Initiated 2011 academic standards petition
- Honorary doctorate: University of Siegen
- Instrument: Cello
Questions readers ask
What is Matthias Kreck's primary area of study?
He specializes in algebraic and differential topology, specifically the classification of manifolds.
Has he led any major mathematical institutions?
Yes, he served as director of the Oberwolfach Research Institute for Mathematics and the Hausdorff Research Institute for Mathematics.
Achievements
- Cantor medal — 2010
- Held posts at University of Bonn, Johannes Gutenberg University Mainz and Heidelberg University
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