# Mikhael Gromov

Wolf Prize Laureate in Mathematics 1993

The Mathematics Prize Committee has unanimously selected the following two scientists to equally share the Wolf Prize for 1993: Jacques Tits and Mikhael Gromov.

**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”.

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.