Mikhael Gromov

Mikhael Gromov Winner of Wolf Prize in Mathematics - 1993
Mikhael Gromov


The Mathematics Prize Committee has unanimously selected the following two scientists to equally share the Wolf Prize for 1993:

Mikhael Gromov
IHES - Institut des Hautes Etudes Scientifiques
Bures-sur-Yvette, France

for his revolutionary contributions to global Riemannian and symplectic geometry, algebraic topology, geometric group theory and the theory of partial differential equations.

Jacques Tits
College de France
Paris, France

for his pioneering and fundamental contributions to the theory of the structure of algebraic and other classes of groups and in particular for the theory of buildings.

Professor Mikhael Gromov has introduced a large number of very original new concepts into the classical field of differential geometry which have led to the solution of a large number of important and apparently unsolvable problems. He has introduced new invariants linking the differential geometric structures with those of algebraic topology which have proved their value both in Gromov´s hands and in the hands of others. He succeeded, for example, in estimating the Betti numbers of Riemannian manifolds solely in terms of a lower bound on the sectional curvature. Much of his work makes use of concepts of the convergence of Riemannian manifolds. These daring ideas are also at the heart of his remarkable solution of the problem of groups of polynomial growth. This geometric approach together with an idea of E. Rips led him to the construction of the theory of hyperbolic groups which has revolutionized the theory of discrete groups. He has also made profound contributions to the global theory of partial differential equations and to the theory of symplectic manifolds, constructing invariants which, for the first time, give a description of the degree of symplectic rigidity. His works are characterized by their incomparable depth and startling originality and will continue to be an inspiration for geometers for many years to come.

Professor Jacques Tits has made many fundamental contributions to the theory of groups and their interactions with geometry. He has developed the theory of buildings as a central organizing principle and powerful tool for an astonishingly wide range of problems in group theory and geometry. This is a geometric approach to group theory which applies to finite groups, to p-adic groups and to arithmetic groups and has been instrumental in many of the most important advances in the last twenty years. Conversely his work also makes use of group theory to make possible many profound contributions to geometry, both by Tits and others. Some of these were areas for which it was not originally designed, such as the theory of Riemannian spaces of rank exceeding 1. Tits ideas are now an essential ingredient in the arsenal of every geometer. Tits has also made many other important contributions to those parts of mathematics listed above, to the theory of Coxeter groups, of Lie groups and of Kac-Moody algebras. The work of Tits has enriched mathematics enormously and has opened the path for numerous further developments.