Matthias Kreck
Encyclopedia
Matthias Kreck 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.
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 diffenertiable 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, he considered examples of asymmetric topological manifolds, finding the first example of such a manifold with trivial fundamental group.
From 1990 to 1998 he was an editor of Mathematischen Annalen and from 1998 to 2002 for Archiv der Mathematik. Since 2000 he has been a member of the Heidelberg Academy of Sciences. In 2003 he was made an honorary doctor of the University of Siegen
. In 2010 he was awarded the Cantor Medal
.
Among his PhD students is Peter Teichner, presently a Director of the Max Planck Institute for Mathematics in Bonn
.
In February 2011 following the "plagiarism scandal" he initiated a "declaration of university professors on academic standards" and the accompanying petition. The original signatories included, e.g. Martin Carrier, Eckhard Freise, Gerhard Huisken und Werner Nahm.
In his spare time he plays the cello
.
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
who works in the areas of Algebraic Topology
Algebraic topology
Algebraic topology is a branch of mathematics which uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphism, though usually most classify up to homotopy equivalence.Although algebraic topology...
and Differential topology
Differential topology
In mathematics, differential topology is the field dealing with differentiable functions on differentiable manifolds. It is closely related to differential geometry and together they make up the geometric theory of differentiable manifolds.- Description :...
. From October 2006 to September 2011 he was the director of the Hausdorff Research Institute for Mathematics at the University of Bonn
University of Bonn
The University of Bonn is a public research university located in Bonn, Germany. Founded in its present form in 1818, as the linear successor of earlier academic institutions, the University of Bonn is today one of the leading universities in Germany. The University of Bonn offers a large number...
where he is currently a professor.
Life and work
Kreck grew up as the son of the theologian Walter Kreck in HerbornHerborn
Herborn is a historic town on the Dill in the Lahn-Dill district of Hesse in Germany. Before World War I, it was granted its own title as Nassauisches Rothenburg. The symbol or mascot of this town is a bear. Scenic attractions include its half-timbered houses; Herborn is located on the German...
and studied mathematics and physics from 1966 to 1970, and business administration at the Universities of Bonn, Berlin and Regensburg.
University of Regensburg
The University of Regensburg is a public research university located in the medieval city of Regensburg, Bavaria, a city that is listed as a UNESCO World Heritage Site. The university was founded on July 18, 1962 by the Landtag of Bavaria as the fourth full-fledged university in Bavaria...
In 1970 he submitted his diploma in Mathematics in Bonn and in 1972 he received his doctorate there under the supervision of Friedrich Hirzebruch
Friedrich Hirzebruch
Friedrich Ernst Peter Hirzebruch is a German mathematician, working in the fields of topology, complex manifolds and algebraic geometry, and a leading figure in his generation.-Life:He was born in Hamm, Westphalia...
(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
University of Wuppertal
The University of Wuppertal is a German scientific institution, located in Wuppertal, North Rhine-Westphalia.The university, the full German name of which is Bergische Universität Wuppertal , was formed in 1972 and is located in the city of Wuppertal, within the state of North Rhine-Westphalia,...
and in 1978 he moved to the University of Mainz. From 1994 to 2002 he was director of the Mathematical Research Institute in Oberwolfach
Mathematical Research Institute of Oberwolfach
The Mathematical Research Institute of Oberwolfach in Oberwolfach, Germany, was founded by mathematician Wilhelm Süss in 1944...
. 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 diffenertiable 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
René Thom
René Frédéric Thom was a French mathematician. He made his reputation as a topologist, moving on to aspects of what would be called singularity theory; he became world-famous among the wider academic community and the educated general public for one aspect of this latter interest, his work as...
, William Browder
William Browder (mathematician)
William Browder is an American mathematician, specializing in algebraic topology, differential topology and differential geometry...
and Dennis Sullivan
Dennis Sullivan
Dennis Parnell Sullivan is an American mathematician. He is known for work in topology, both algebraic and geometric, and on dynamical systems. He holds the Albert Einstein Chair at the City University of New York Graduate Center, and is a professor at Stony Brook University.-Work in topology:He...
. 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, he considered examples of asymmetric topological manifolds, finding the first example of such a manifold with trivial fundamental group.
From 1990 to 1998 he was an editor of Mathematischen Annalen and from 1998 to 2002 for Archiv der Mathematik. Since 2000 he has been a member of the Heidelberg Academy of Sciences. In 2003 he was made an honorary doctor of the University of Siegen
University of Siegen
The University of Siegen in Siegen, North Rhine-Westphalia, was founded in 1972. 14,100 students were enrolled at the university as of October 2010.-Faculties:University of Siegen offers in total 126 degree programmes across four faculties:...
. In 2010 he was awarded the Cantor Medal
Cantor medal
The Cantor medal of the Deutsche Mathematiker-Vereinigung is named in honor of Georg Cantor. It is awarded at most every second year during the yearly meetings of the society...
.
Among his PhD students is Peter Teichner, presently a Director of the Max Planck Institute for Mathematics in Bonn
Bonn
Bonn is the 19th largest city in Germany. Located in the Cologne/Bonn Region, about 25 kilometres south of Cologne on the river Rhine in the State of North Rhine-Westphalia, it was the capital of West Germany from 1949 to 1990 and the official seat of government of united Germany from 1990 to 1999....
.
In February 2011 following the "plagiarism scandal" he initiated a "declaration of university professors on academic standards" and the accompanying petition. The original signatories included, e.g. Martin Carrier, Eckhard Freise, Gerhard Huisken und Werner Nahm.
In his spare time he plays the cello
Cello
The cello is a bowed string instrument with four strings tuned in perfect fifths. It is a member of the violin family of musical instruments, which also includes the violin, viola, and double bass. Old forms of the instrument in the Baroque era are baryton and viol .A person who plays a cello is...
.
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 1069th 1984 (Appendix by Neal Stoltzfus)
- Exotic structures on 4-manifolds, annual report, DMV, Bd.88, 1986, pp. 124–145
- With Wolfgang LückWolfgang LückWolfgang Lück is a German mathematician who is an internationally recognized expert in Algebraic Topology.- Life and work :...
: The Novikov Conjecture – geometry and algebra, Birkhäuser 2005 (Oberwolfach Seminar) - Positive curvature and topology, NY Academy of Sciences, Opladen, West German Verlag 1994
- Kreck, Hambleton: On the classification of topological 4-manifolds with finite fundamental group Mathematische Annalen, Bd 280, 1988, p. 85
- Kreck, Lück, Teichner: Counterexamples of the Kneser conjecture in dimension 4 Comm.Math.Helveticae Bd.70, 1995, S.423