William Goldman (mathematician)
William Mark Goldman (born November 17, 1955 in Kansas City , Missouri ) is an American mathematician who studies geometry.
Goldman graduated from Princeton University with a bachelor's degree in 1977 and received his doctorate in 1980 from the University of California, Berkeley with Morris W. Hirsch (and William Thurston ) ( Discontinuous groups and the Euler class ). As a post-doctoral student at the University of Colorado , he was a Moore Instructor at the Massachusetts Institute of Technology from 1981 to 1983 . He was then an assistant professor at MIT until 1986. He has been Associate Professor since 1986 and Professor at the University of Maryland in College Park from 1990 . There he is director and co-founder of the Experimental Geometry Lab, which develops software for the study of low-dimensional manifolds.
He was visiting scholar at MSRI and the Institute for Advanced Study (2008) and visiting professor at Oxford in 1989. In 2010 he was invited speaker at the International Congress of Mathematicians in Hyderabad ( Locally homogeneous geometric manifolds ).
Since his master's thesis he has been dealing with various geometric structures on manifolds and their classification. For example, with Suhyoung Choi he classified real projective structures on compact surfaces .
In 1983, together with David Fried, he classified affine crystallographic groups in three dimensions, expanding the classic case of Schoenflies and Fjodorow for isometries to affine transformations.
From 2003 to 2013 he was editor of Geometriae dedicata.
In 1987 he became a research fellow of the Alfred P. Sloan Foundation ( Sloan Research Fellow ). In 2012 he became a Fellow of the American Mathematical Society .
Bernhard Leeb is one of his doctoral students .
Fonts
- Complex hyperbolic geometry , Clarendon Press, Oxford 1999
- Locally homogeneous geometric manifolds , ICM 2010
- with Morris Hirsch : A generalization of Bieberbach's theorem , Invent. Math. 65, 1981/82, pp. 1-11
- with David Fried : Three-dimensional affine crystallographic groups , Adv. in Math. 47, 1983, no. 1, pp. 1-49
- The symplectic nature of fundamental groups of surfaces , Advances in Mathematics 54, 1984, pp. 200-225
- Invariant functions on Lie groups and Hamiltonian flows of surface group representations , Invent. Math. 85, 1986, pp. 263-302
- with John Millson : Local rigidity of discrete groups acting on complex hyperbolic space , Invent. Math. 88, 1987, no. 3, pp. 495-520
- Topological components of spaces of representations , Invent. Math. 93, 1988, pp. 557-607
- with John Millson: The deformation theory of representations of fundamental groups of compact Kähler manifolds , Inst. Hautes Études Sci. Publ. Math. No. 67, 1988, pp. 43-96
- Convex real projective structures on compact surfaces , Journal of Differential Geometry 31, 1990, pp. 791-845
- with Suhyoung Choi : Convex real projective structures on closed surfaces are closed , Proc. Amer. Math. Soc. 118, 1993, no. 2, pp. 657-661
- Ergodic theory on moduli spaces , Annals of Mathematics, Volume 146, 1997, pp. 475-507
- The modular group action on real SL (2) characters of a one-holed torus , Geom. Topol. 7, 2003, pp. 443-486
- What is a projective structure? , Notices AMS, 2007, No. 1
- with François Labourie , Grigori Margulis : Proper affine actions and geodesic flows of hyperbolic surfaces , Ann. of Math. (2) 170, 2009, no. 3, pp. 1051-1083
Web links
Individual evidence
- ^ Mathematics Genealogy Project
- ↑ Choi, Goldman The Classification of Real Projective Structures on compact surfaces , Bull. Amer. Math. Soc. 34 (2), 1997, pp. 161-170, online
- ^ Fried, Goldman: Three-dimensional affine crystallographic groups , Advances in Mathematics 47, 1983, pp. 1-49
| personal data | |
|---|---|
| SURNAME | Goldman, William |
| ALTERNATIVE NAMES | Goldman, William Mark (full name) |
| BRIEF DESCRIPTION | American mathematician |
| DATE OF BIRTH | 17th November 1955 |
| PLACE OF BIRTH | Kansas City (Missouri) |