Peter Teichner

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Peter Teichner

Peter Teichner (born June 30, 1963 in Bratislava , Czechoslovakia ) is a mathematician. Since 2008 he has been director at the Max Planck Institute for Mathematics in Bonn. His main areas of work are topology and geometry .

biography

Peter Teichner graduated from Gutenberg University Mainz in 1988 with a degree in mathematics. After graduating, he worked in Canada for a year , funded by the Government of Canada Award, at McMaster University in Hamilton (Ontario) . From 1989 to 1990 he worked at the Max Planck Institute for Mathematics . From 1990 to 1992 he worked at the University of Mainz as a research assistant , in 1992 he did his doctorate there under Matthias Kreck . The title of his doctoral thesis was: Topological four-manifolds with finite fundamental group . With the Feodor Lynen Fellowship, which he received from the Humboldt Foundation , he conducted research at UC San Diego from 1992 to 1995 in collaboration with Michael Freedman . In 1995 he conducted research at the Institut des Hautes Études Scientifiques in Bures-sur-Yvette , France . From 1995 to 1996 he worked again at the University of Mainz. From 1996 to 1997 he was at UC Berkeley with a Miller Research Fellow. From 1996 he was employed as an associate professor at UC San Diego for three years , from 1999 he was appointed full professor (corresponds to the German W3 professor). He stayed at UC San Diego until 2004 and has been a full professor at UC Berkeley since then. In 2007 he conducted research again at the Institut des Hautes Études Scientifiques . Since 2008 he has been director at the Max Planck Institute for Mathematics in Bonn. Since 2011 he has also been Managing Director.

research

Peter Teichner works in the research field of topology , in which he investigates qualitative properties of n-dimensional spaces.

His first focus is the investigation of the 4th dimension and the classification of 4- manifolds . His motivation here comes from physics , since the universe has 4 dimensions. In cooperation with theoretical physics it is his goal to find out which manifolds there are and which have the properties of the universe. Together with Fields medalist Mike Freedman , Peter Teichner has made contributions to the classification of 4-manifolds, whose fundamental group only grows sub-exponentially. The fundamental group is the most important qualitative invariant of abstract spaces, it describes closed geodesics . Teichner works on precise classification results, including a. hoping to come across a description of space-time : This is an example of a 4-manifold and if it is compact and its fundamental group is not too complicated, then space-time has to appear in the classification list, at least its topological model. Which model is the right one should then be able to be decided by physical properties. Since many questions have already been answered mathematically in the area of ​​the 4th dimension , he turned to his second focus, the Euclidean and topological field theories . In another project, Peter Teichner and Stephan Stolz try to define the mathematical concept of a quantum field theory in such a way that deformation classes of quantum field theories can be interpreted as a qualitative property of a manifold. More precisely, these should form a cohomology theory , such as e.g. B. De-Rham cohomology , K-theory or elliptical cohomology. In the first two cases, this has already been achieved with the help of supersymmetric quantum field theories; the elliptical case is still open. This research is to be understood analogously to that on manifolds in such a way that the real existing examples (e.g. space-time or QED ) are reduced to their core content and can thus be generalized. The resulting language should be flexible enough to formulate new physical theories, but also so precise that predictions can be made about the impossibility of certain combinations of space-time and quantum fields.

Billiards game

An example of why one is interested in topology beyond the 4th dimension . The table of a billiard game has two dimensions : length and width. It's easy to give the coordinates of each ball on the table. But you need 4 dimensions to know exactly where the ball is on the table and which point (s) on the surface of the ball (= additional 2 dimensions) touches the table. So there are 4 dimensions for a sphere. Since all spheres are independent of each other, you need 4 dimensions for each sphere. A billiard game is played with 15 balls, so you have to work with (15 × 4 =) 60 dimensions. In order to be able to describe physical situations well, one needs more dimensions than 2 or 3.

Big lectures

Organized Conferences

Publications (selection)

  • Teichner What is a Grope? , Notices American Mathematical Society, September 2004, online
  • Teichner, Stephan Stolz Supersymmetric field theories and generalized cohomology , Preprint, 2011, to appear in Mathematical Foundations of Quantum Field Theory and Perturbative String Theory, Proceeding of the AMS, 2011
  • Kreck, Matthias; Lück, Wolfgang ; Teichner, Peter Stable prime decompositions of four-manifolds. Prospects in topology (Princeton, NJ, 1994), 251-269, Ann. of Math. Stud., 138, Princeton Univ. Press, Princeton, NJ, 1995.
  • Freedman, Michael H .; Teichner, Peter 4-manifold topology. II. Dwyer's filtration and surgery kernels. Invent. Math. 122 (1995) no. 3, 531-557. On-line
  • Freedman, Michael H .; Teichner, Peter 4-manifold topology. I. Subexponential groups. Invent. Math. 122 (1995) no. 3, 509-529. On-line
  • Kreck, Matthias; Lück, Wolfgang; Teichner, Peter Countere examples of the Kneser conjecture in dimension four. Comment. Math. Helv. 70 (1995) no. 3, 423-433. On-line
  • Teichner, Peter 6-dimensional manifolds without totally algebraic homology. Proc. Amer. Math. Soc. 123 (1995) no. 9, 2909-2914.
  • Freedman, Michael H .; Krushkal, Vyacheslav S .; Teichner, Peter van Kampen's embedding obstruction is incomplete for 2-complexes in R4. Math. Res. Lett. 1 (1994) no. 2, 167-176.
  • Hambleton, Ian; Kreck, Matthias; Teichner, Peter Nonorientable 4-manifolds with fundamental group of order 2. Trans. Amer. Math. Soc. 1994, 344, no. 2, 649-665.
  • Teichner, Peter On the signature of four manifolds with universal covering spin. Math. Ann. 295 (1993) no. 4, 745-759. On-line

Web links

Individual evidence

  1. ^ Proc. ICM Beijing, II, p. 437, online
personal data
SURNAME Teichner, Peter
BRIEF DESCRIPTION Slovak mathematician
DATE OF BIRTH June 30, 1963
PLACE OF BIRTH Bratislava