Thomas Schick

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Thomas Schick (born May 22, 1969 in Alzey ) is a German mathematician who deals with algebraic topology and differential geometry.

Thomas Schick, Oberwolfach 2012

Schick studied mathematics and physics at the Johannes Gutenberg University Mainz , where he received his diploma in mathematics in 1994 and his doctorate in 1996 under Wolfgang Lück ( Analysis on Manifolds of Bounded Geometry, Hodge-deRham Isomorphism and -Index Theorem ). As a post-doctoral student he spent two years at the University of Münster and from 1998 to 2000 as an assistant professor at the Pennsylvania State University (with Nigel Higson and John Roe ). Schick completed his habilitation in Münster in 2000 and has been Professor of Pure Mathematics at the Georg-August University in Göttingen since 2001 .

He deals with topological invariants, e.g. B. -invariants and those that result from the K-theory of operator algebras . You step z. B. in generalizations of the Atiyah-Singer index rate .

With Wolfgang Lück he introduced the strong Atiyah conjecture. The Atiyah conjecture makes statements about the possible values ​​of the -Betti numbers of Riemann manifolds and general CW complexes (depending on the properties of the fundamental group ). With Peter Linnell, Schick proved a theorem about the behavior in group expansions and he proved special cases. He also used similar methods with the Baum-Connes conjecture , where he proved a theorem about the validity when extending groups, for which the validity has already been proven, with application to braid groups .

After the Gromov-Lawson-Rosenberg conjecture for criteria for the existence of a metric with positive scalar curvature was proven for a number of fundamental groups in the 1990s , Schick found a counterexample in 1997.

He was the coordinator of the Courant Research Center for Higher Order Structures in Mathematics at the University of Göttingen. One of the main goals of the research center was to study mathematical structures that could play a role in modern theoretical physics ( string theory , quantum gravity ).

He is on the editorial board of the Mathematische Annalen . In 2014 he was invited speaker at the ICM in Seoul (The topology of scalar curvature). He has been a full member of the Göttingen Academy of Sciences since 2016 .

Fonts

  • Topology of scalar curvature. Proc. ICM 2014, Seoul.
  • Operator algebras and topology. ICTP Summer School, Trieste 2001.
  • With Bunke : Differential K-Theory.
  • With Bunke : Smooth K-Theory. In: Astérisque. No. 328 (2009), 45-135 (2010). ISBN 978-2-85629-289-1 .
  • With Hanke , Steimle: The space of metrics of positive scalar curvature. Publ. Math. Inst. Hautes Études Sci. 120 (2014), 335-367.
  • With Hanke: Enlargeability and index theory. J. Differential Geom. 74 (2006), no. 2, 293-320.
  • With Dodziuk, Linnell, Mathai, Yates: Approximating L2-invariants and the Atiyah conjecture. Dedicated to the memory of Jürgen K. Moser . Comm. Pure Appl. Math. 56 (2003), no. 7, 839-873.
  • With Grigorchuk , Linnell, Żuk: On a question of Atiyah. CR Acad. Sci. Paris Sér. I Math. 331 (2000), no. 9, 663-668.
  • With Lück : torsion of hyperbolic manifolds of finite volume. In: Geometric and Functional Analysis. Volume 9, 1999, pp. 518-567, Arxiv.
  • Integrality of Betti numbers. In: Mathematical Annals. Volume 317, 2000, pp. 727-750, Arxiv.
  • -index theorem for elliptic boundary problems. In: Pacific J. Math. Volume 197, 2001, pp. 423-439, Arxiv.

Web links

Individual evidence

  1. ^ Mathematics Genealogy Project
  2. ^ Schick, Linnell: Finite group extensions and the Atiyah conjecture. In: Journal of the American Mathematical Society. Volume 20, 2007, pp. 1003-1061, website by Schick about this.
  3. ^ For example, Schick: Integrality of Betti numbers. In: Mathematical Annals. Volume 317, 2000 p. 727.
  4. ^ Schick: Finite group extensions and the Baum-Connes conjecture. In: Geom. Topol. 11: 1767-1775 (2007). Preprint.
  5. ↑ Schick's website on this.
  6. ↑ Named after H. Blaine Lawson , Michail Leonidowitsch Gromow , Jonathan Rosenberg
  7. ↑ Schick: A counterexample to the (unstable) Gromov-Lawson-Rosenberg conjecture. In: Topology. Volume 37, 1998, pp. 1165-1168, Preprint.
  8. ↑ Göttinger Tagblatt on the newly opened Courant Research Center, 2009.
personal data
SURNAME Schick, Thomas
BRIEF DESCRIPTION German mathematician
DATE OF BIRTH May 22, 1969
PLACE OF BIRTH Alzey