William Goldman (mathematician)
William Mark Goldman ( born 1955 in Kansas City ) is an American mathematician who is concerned with geometry.
Goldman studied at Princeton University with a bachelor's degree in 1977 and in 1980 at the University of California, Berkeley with Morris W. Hirsch ( and William Thurston ) PhD (Discontinuous groups and the Euler class ). As a post - graduate student he was at the University of Colorado and 1981-1983 Moore Instructor at Massachusetts Institute of Technology. He was then to 1986 Assistant Professor at MIT. Since 1986 he is an associate professor and in 1990 professor at the University of Maryland at College Park. There he is director and co-founder of the Experimental Geometry Lab, developed the software for the study of low dimensional manifolds.
He was a visiting scientist at MSRI and the Institute for Advanced Study ( 2008) and 1989 Visiting Professor at Oxford. In 2010 he was invited speaker at the International Congress of Mathematicians in Hyderabad ( Locally homogeneous geometric manifolds ).
He has been working for his diploma thesis with various geometric structures on manifolds and their classification. For example, he classified with Suhyoung Choi real projective structures on compact surfaces.
In 1983, he classified with David Fried affine crystallographic groups in three dimensions, the classic case of Schoenflies and Fyodorov for isometrics to affine transformations expanding.
2003 to 2013 he was editor of Geometriae dedicata.
In 2012 he became a Fellow of the American Mathematical Society.
Writings
- 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.
- David Fried: Three-dimensional affine crystallographic groups. Adv in Math 47 (1983 ), no 1, 1-49.
- The symplectic nature of fundamental groups of surfaces, Advances in Mathematics 54 (1984) 200-225
- Invariant functions on Lie groups and Hamiltonian flows of surface group representations, Invent. Math 85 (1986) 263-302
- With John Millson: Local rigidity of discrete groups acting on complex hyperbolic space. Invent. Math 88 (1987 ), no 3, 495-520.
- Topological components of spaces of representations, Invent. Math 93 (1988) 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), 43-96.
- Convex real projective structures on compact surfaces, Journal of Differential Geometry 31 (1990 ), 791 - 845
- With Suhyoung Choi: Convex real projective structures on closed surfaces are closed. Proc. Amer. Math Soc. 118 (1993), no 2, 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), 443-486.
- What is a projective structure? , Notices AMS, 2007, No.1
- With François Labourie, Grigory Margulis: Proper affine actions and geodesic flows of hyperbolic surfaces. Ann. of Math ( 2) 170 (2009 ), no 3, 1051-1083.