Education
In 1980 he received a Doctor of Philosophy from the University of Bonn with under the supervision of Stefan Hildebrandt.
In 1980 he received a Doctor of Philosophy from the University of Bonn with under the supervision of Stefan Hildebrandt.
He has been a director of the Max Planck Institute for Mathematics in the Sciences in Leipzig since 1996. In 1975, he began studying mathematics, physics, economics and philosophy. In 1984 he was at the University of Bonn for the habilitation.
After his habilitation, he was at the Ruhr-University Bochum, the chair of Mathematics X, Analysis.
During this time he was the coordinator of the project "Stochastic Analysis and systems with infinitely many degrees of freedom" July 1987 to December 1996. Since 1996, he has been director and scientific member at the Max Planck Institute for Mathematics in the Sciences in Leipzig.
After more than 10 years of work in Bochum, this he followed: "tackle new research problems in the border area between mathematics and the natural sciences and simultaneously encourage mathematical research in Germany, particularly in the fields of geometry and analysis."
In 1998 he was an honorary professor at the University of Leipzig. In 2002, there, he initiated with two other scientists from the Max Planck Institute, the Interdisciplinary Center for Bioinformatics (IZBI).
In 1986 he was invited speaker at the International Congress of Mathematicians in Berkeley (Two dimensional geometric variational problems).
He is a fellow of the American Mathematical Society. His research focuses are:
Complex dynamic systems
Neural networks
Cognitive structures and theoretical neurobiology, cognitive science, theoretical and mathematical biology
Riemannian geometry. Analysis and geometry
Calculus of variations and partial differential equations.
Mathematical physics.
Publications Harmonic mappings between Riemannian manifolds, ANU press, Canberra, 1983 Harmonic maps between surfaces, Springer LNM 1062, 1984, , doi:10.1007/BFb0100160 Nonlinear methods in complex geometry, Birkh�user, Basel, Boston, series: DMV seminars, vol. 10, 1988
2Nd Edition 1991 Two dimensional geometric achieved problem, Wiley-InterScience, Chichester, 1991, Differential Geometry and Minimal Surfaces, Springer, 1994. 2Nd Edition 2007 (with j-H) Eschenburg), , doi:10.1007/978-3-540-68293-6 Riemannian Geometry and Geometric Analysis, Springer, 1995.
6Th Edition 2011, , doi:10.1007/978-3-642-21298-7 Compact Riemann Surfaces, Springer, 1997. 3. Edition 2006, , doi:10.1007/978-3-540-33067-7 Postmodern Analysis, Springer, 1905, 3rd Edition 2005, , doi:10.1007/3-540-28890-2 A mathematical introduction to string theory - achieved problem, geometric and probabilistic methods (with S Albeverio, S Paycha S Scarlatti), London math. Soc., lecture note series 225, Cambridge Univ.
Press, 1997, Calculus of Variations (with x Li-Jost), Cambridge Univ. Press, 1998, Nonpositive curvature: geometric and analytic aspects, (lectures in mathematics: ETH Zurich), Birkh�user-Verlag, Basel, 1997, Partial Differential Equations, Springer, 1998, , doi:10.1007/978-3-642-58888-4 Bosonic Strings: A mathematical treatment, AMS international press, 2001 Partial Differential Equations, Springer, 2002, 3rd Edition in 2013, , doi:10.1007/978-1-4614-4809-9 Dynamical Systems. Examples of complex behaviour, Springer, 2005, , doi:10.1007/3-540-28889-9 Geometry and Physics, Springer, 2009, , doi:10.1007/978-3-642-00541-1.
Saxonian Academy of Sciences. German Academy of Sciences Leopoldina. American Mathematical Society.
Akademie der Wissenschaften und der Literatur.