George Mostow

George Daniel Mostow ( born July 4, 1923) is an American mathematician who deals primarily with differential geometry, algebraic groups and Lie groups.

Life

Mostow studied at Harvard University, where he received his doctorate at Garrett Birkhoff 1948 (The extensibility of local Lie Groups of Transformations and Groups on Surfaces ). From 1952 he was a professor at Yale University, where he retired in 1999 at Johns Hopkins University and from 1961.

1957 was Mostow Guggenheim Fellow. He is since 1974 a member of the National Academy of Sciences and was 1987/8 president of the American Mathematical Society. In 1993 he received the Leroy P. Steele Prize for achievements in research and his book Strong rigidity in locally symmetric spaces of 1973. 1970 he was Invited Speaker at the International Congress of Mathematicians in Nice (The rigidity of locally symmetric spaces ). In 2013 he was awarded the Wolf Prize in Mathematics.

Work

He discovered and examined rigidity properties of lattices in semisimple Lie groups (without compact factor groups and centers ), that is, discrete subgroups of semisimple Lie groups, so that the quotient space of the Lie group modulo the discrete subgroup compact. Its rigidity theorem from 1972 states that isomorphisms of the lattice can be expanded in these Lie groups on analytic isomorphisms of Lie groups, except for. Applied to hyperbolic spaces it says that hyperbolic manifolds finite volume are clearly defined in more than two dimensions by their fundamental group. Mostow's work revived the study of symmetric spaces ( William Thurston's classification of three-dimensional manifolds ) and were based more rigidity sets, for example, by Grigori Aleksandrovich Margulis, Mostow 1974 the building on the Arithmetizität of lattices in semisimple Lie groups of rank > 1 proved.

Writings

With Pierre Deligne: Commensurabilities among lattices in. Annals of Mathematical Studies, Princeton University Press 1993.
With Deligne: monodromy of hypergeometric functions and nonlattice integral monodromy. Inst Hautes Études Sci. Publ Math No. 63 (1986), 5-89.
Generalized Picard lattices Arising from half- integral conditions. Inst Hautes Études Sci. Publ Math No. 63 (1986), 91-106.
Yum - Tong Siu: A compact Kähler surface of negative curvature not covered by the ball. Ann. of Math ( 2) 112 (1980 ), no 2, 321-360.
On a remarkable class of polyhedra in complex hyperbolic space. Pacific J. Math 86 (1980 ), no 1, 171-276.
Strong rigidity of locally symmetric spaces. Annals of Mathematical Studies, Princeton 1973.
Quasi - conformal mappings in n -space and the rigidity of hyperbolic space forms. Inst Hautes Études Sci. Publ Math No. 34 1968 53-104.
Cohomology of topological groups and solvmanifolds. Ann. of Math ( 2) 1961 73 20-48.
Equivariant embeddings in Euclidean space. Ann. of Math ( 2) 65 (1957 ), 432-446.
Fully reducible subgroups of algebraic groups. Amer. J. Math 78 (1956 ), 200-221.
Some new decomposition theorems for semi -simple groups. Mem Amer. Math Soc. 1955 ( 1955). no 14, 31-54.
Factor spaces of solvable groups. Ann. of Math ( 2) 60, (1954). 1-27.

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