Werner Ballmann

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Werner Ballmann

Hans Werner Ballmann (born April 11, 1951 in Hillesheim ) is a German mathematician who deals with differential geometry and global analysis .

Life

Werner Ballmann studied mathematics at the University of Bonn . He earned his graduate degree in 1976 and was in 1979 Wilhelm Klingenberg doctorate ( Some new results on manifolds of non-positive curvature ). He was then a research assistant in Bonn, where he completed his habilitation there in 1984, was a post-doctoral student at the University of Pennsylvania in Philadelphia in 1980/81 and, from 1984, an associate professor at the University of Maryland in College Park. In 1986 he became associate professor in Bonn and then in 1987 full professor at the University of Zurich . As successor to Wilhelm Klingenberg, he held the chair for differential geometry at the University of Bonn from 1989 to 2016. From 2007 to 2019 he was director at the Max Planck Institute for Mathematics .

From 1996 to 1999 Werner Ballmann was spokesman for the Collaborative Research Center Nonlinear Partial Differential Equations (SFB 256), from 2003 to 2010 member of the Presidium of the German Mathematicians Association (DMV), from 2004 to 2012 member of the Council of the Mathematical Research Institute Oberwolfach , from 2009 to 2015 Member of the board of directors of the Institut des Hautes Études Scientifiques in Bures-sur-Yvette and from 2009 to 2012 coordinator of the Hausdorff Center for Mathematics in Bonn. He was co-editor of several scientific journals, including Inventiones mathematicae from 1996 to 2007.

Werner Ballmann was invited to speak at the International Congress of Mathematicians in Berkeley in 1986 (Manifolds of nonpositive sectional curvature and manifolds without conjugate points). He has been a member of the Leopoldina since 2007 . In May 2017 he gave the Gauß lecture of the DMV in Kiel.

His students include Christian Bär , Vicente Cortés, Alexander Lytchak, Dorothee Schüth, Gregor Weingart and Anna Wienhard .

plant

Werner Ballmann deals with differential geometry and global analysis. Among other things, he investigated closed geodesics, the structure of spaces of non-positive curvature and applications in geometric group theory, the Laplace equation with Dirichlet boundary conditions at infinity on spaces of non-positive curvature and the spectrum of Dirac and Laplace operators. One of its main results is the so-called rigidity of rank theorem . This theorem says that a complete Riemannian manifold of non-positive bounded curvature and finite volume of rank at least two is locally a symmetric space or a product.

Fonts

  • Introduction to geometry and topology , Basel: Birkhäuser 2015, ISBN 978-3-0348-0900-9 .
  • Lectures on Kähler manifolds , ESI Lectures in Mathematics and Physics. EMS Publishing House 2006, ISBN 978-3-0371-9025-8 .
  • Lectures on spaces of non positive curvatures (PDF; 818 kB), DMV Seminar, Birkhäuser 1995.
  • Spaces of non positive curvature , Annual Report DMV, Volume 103, 2001, pp. 52-65.
  • with J. Swiatkowski: On cohomology and property (T) for automorphism groups of polyhedral cell complexes. Geom. Funct. Anal. 7 (1997), no. 4, 615-645.
  • with M. Brin: Orbihedra of nonpositive curvature. Inst. Hautes Études Sci. Publ. Math. No. 82: 169-209 (1996) (1995).
  • Nonpositively curved manifolds of higher rank , Ann. of Math. 122: 597-609 (1985).
  • with G. Thorbergsson and W. Ziller, Closed geodesics on positively curved manifolds , Ann. of Math. 116: 213-247 (1982).
  • The sentence by Lusternik and Schnirelmann , Bonner Mathematische Schriften, Volume 102, 1978, pp. 1-25.

Web links

Individual evidence

  1. ↑ see Werner Ballmann: Spaces with negative curvature (article about Ballmann in the 2007 annual report of the Max Planck Society), page 5 PDF, accessed April 15, 2020
  2. ↑ Member entry by Werner Ballmann (with picture) at the German Academy of Natural Scientists Leopoldina , accessed on June 29, 2016.
personal data
SURNAME Ballmann, Werner
ALTERNATIVE NAMES Ballmann, Hans Werner
BRIEF DESCRIPTION German mathematician
DATE OF BIRTH April 11, 1951
PLACE OF BIRTH Hillesheim