Stephan Stolz

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Stephan A. Stolz (born November 5, 1954 ) is a German mathematician who deals with geometric topology and differential geometry.

Stephan Stolz, Oberwolfach 2009

Life

Stolz studied mathematics at Bielefeld University (pre-diploma in 1975) and Bonn University with a diploma in 1979 ( relationships between transfer and J-homomorphism ) and received his doctorate in 1984 from Johannes Gutenberg University Mainz under Matthias Kreck ( investigation of highly related manifolds and their edges ). He is a professor at the University of Notre Dame .

In 1995 he and Jonathan Rosenberg introduced a stable version of the conjecture by Gromov , Lawson, and Rosenberg about the existence of metrics with positive scalar curvature . In 1992 he proved the Gromov-Lawson conjecture for simply connected manifolds and other special cases of the conjecture.

He works with Peter Teichner on applications of supersymmetric and other quantum field theories in topology.

In 1994 he was invited speaker at the International Congress of Mathematicians in Zurich ( Positive scalar curvature metrics - existence and classification questions ).

Fonts

  • with Peter Teichner: Supersymmetric field theories and generalized cohomology . In: Hisham Sati, Urs Schreiber (Ed.): Mathematical foundations of quantum field theory and perturbative string theory , Proc. Sympos. Pure Math. 83, American Mathematical Society, 2011, pp. 279-340, arxiv : 1108.0189
  • with Peter Teichner: What is an elliptic object? In: Topology, Geometry and Quantum Field Theory , Cambridge University Press, 2004, pp. 247-343.
  • with Jonathan Rosenberg: Manifolds of positive scalar curvature . In: GE Carlsson, RL Cohen, W.-C. Hsiang, JDS Jones (Ed.): Algebraic topology and its applications . In: MSRI publications 27. Springer-Verlag, 1994, pp. 241-267
  • Simply connected manifolds of positive scalar curvature . In: Ann. of Math. (2) 136, 1992, no. 3, pp. 511-540.
  • with Matthias Kreck: Some homeomorphic but not diffeomorphic homogeneous 7-manifolds with positive sectional curvature . In: J. of Diff. Geometry , Vol. 33, 1991, pp. 465-486
  • with Matthias Kreck: Non-connected moduli spaces of positive sectional curvature metrics . In: Jour. of Amer. Math. Soc. , Volume 6, 1994, pp. 825-850, 1993
  • with Matthias Kreck: HP 2-bundles and elliptic homology . In: Acta Mathematica , Volume 171, 1993, pp. 231-261
  • with William Dwyer, Thomas Schick : Remarks on a conjecture of Gromov and Lawson . In: Farrell, Wolfgang Lück (Ed.): High-dimensional manifold topology (Proceedings of the school held in Trieste, May 21 - June 8, 2001). World Scientific, 2003, pp. 159-176, arxiv : math / 0208011

Web links

Individual evidence

  1. ^ Mathematics Genealogy Project . The dissertation was published in Lecture Notes in Mathematics , Volume 1116, Springer Verlag 1985
  2. ↑ Gromov-Lawson_conjecture Gromov-Lawson Conjecture , Encyclopedia of Mathematics
  3. ^ Rosenberg, Stolz: A "stable" version of the Gromov-Lawson conjecture . In: Contemp. Mathematics , Volume 181, 1995, pp. 405-418, arxiv : dg-ga / 9407002
  4. ↑ Proud: Simply connected manifolds of positive scalar curvature . In: Annals of Mathematics , Volume 136, 1992, pp. 511-540.
  5. ↑ B. Botvinnik, Peter Gilkey , S. Stolz: The Gromov – Lawson – Rosenberg conjecture for groups with periodic cohomology . In: J. Diff. Geom. , Vol. 46, 1997, pp. 374-405
personal data
SURNAME Proud, Stephan
ALTERNATIVE NAMES Stolz, Stephan A.
BRIEF DESCRIPTION German mathematician
DATE OF BIRTH 5th November 1954