Matthias Kreck

Matthias Kreck (born 22 July 1947 in Dillenburg) is a German mathematician who works in the areas of Algebraic Topology and Differential topology. From October 2006 to September 2011 he was the director of the Hausdorff Research Institute for Mathematics at the University of Bonn where he is currently a professor.

Kreck grew up as the son of the theologian in Herborn and studied mathematics and physics from 1966 to 1970, and business administration at the Universities of Bonn, Berlin and Regensburg. In 1970 he submitted his diploma in Mathematics in Bonn and in 1972 he received his doctorate there under the supervision of Friedrich Hirzebruch (An invariant for stably parallelized manifolds). From 1972 to 1976 he studied Protestant theology in Bonn: in a similar period he was also assistant from 1970 to 1976 to professor Hirzebruch. In 1977 he completed his habilitation in Bonn in Mathematics (Bordism groups of diffeomorphisms). In 1976 he became professor at the Wuppertal University and in 1978 he moved to the University of Mainz. From 1994 to 2002 he was director of the Mathematical Research Institute in Oberwolfach. In 1999 he became professor at the University of Heidelberg. From 2007 until October 2011 he was the founding director of the Hausdorff Research Institute for Mathematics at the University of Bonn. In 1981/82 and from 1989 to 1992 he was visiting professor at the Max Planck Institute for Mathematics in Bonn. He was also a guest researcher at places including Paris, Princeton, Berkeley, Chicago, Aarhus, St. Petersburg, Moscow and Beijing.

Kreck worked on the classification of manifolds in differential topology (e.g. bordism groups), 4-manifolds with exotic differentiable structure and the interaction of differential geometry and topology. In his habilitation in 1977 he managed the complete classification of closed smooth manifolds with diffeomorphisms up to bordism: a problem that had already been worked on by René Thom, William Browder and Dennis Sullivan. Building on this work he developed a modified theory of surgery which is applicable under weaker conditions than classical surgery and he applied this theory to solve outstanding questions in differential geometry. In the 2000s (decade), he considered examples of asymmetric topological manifolds, finding the first example of such a manifold with trivial fundamental group.

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