**Furstenberg**和**Smale**教授荣获2006/7年度沃尔夫数学奖

（转自**沃尔夫基金会官方网站**）

**沃尔夫基金会官方网站**公布2006/7年度沃尔夫数学奖的获得者是**Harry Furstenberg**教授（**Hebrew University of
Jerusalem**）和**Stephen
Smale** 教授(**University of
California, Berkeley**)。两位获奖者将分享十万美元的奖金。颁奖仪式将于

**THE 2006/7 WOLF FOUNDATION PRIZE IN
MATHEMATICS**

The
Prize Committee for Mathematics has unanimously decided that the 2006/7 Wolf
Prize will be jointly awarded to:

**Harry Furstenberg** (The Hebrew

for his profound contributions to ergodic theory, probability, topological dynamics, analysis
on symmetric spaces and homogenous flows.

Harry Furstenberg (1935,

Professor Harry
Furstenberg is one of the great masters of probability theory, ergodic theory and topological dynamics. Among his
contributions: the application of ergodic theoretic
ideas to number theory and combinatorics and the
application of probabilistic ideas to the theory of Lie groups and their
discrete subgroups.

In probability
theory he was a pioneer in studying products of random matrices and showing how
their limiting behavior was intimately tied to deep structure theorems in Lie
groups. This result has had a major influence on all subsequent work in this
area--which has emerged as a major branch not only in probability, but also in
statistical physics and other fields.

In topological
dynamics, Furstenberg抯 proof of the structure theorem for minimal distal flows, introduced
radically new techniques and revolutionized the field. His
theorem that the horocycle flow on surfaces of
constant negative curvature is uniquely ergodic, has
become a major part of the dynamical theory of Lie group actions. In his
study of stochastic processes on homogenous spaces, he introduced stationary
methods whose study led him to define what is now called the Furstenberg
Boundary of a group. His analysis of the asymptotic behavior of random walks on
groups, has had a lasting influence on subsequent work
in this area, including the study of lattices in Lie groups and co-cycles of
group actions.

In ergodic theory, Furstenberg developed the fundamental
concept of dynamical embedding. This led him to spectacular applications in combinatorics, including a new proof of the Szemeredi Theorem on arithmetical progressions and
far-reaching generalizations thereof.

**Stephen J. Smale**** **(

for his groundbreaking contributions that
have played a fundamental role in shaping differential topology, dynamical
systems, mathematical economics, and other subjects in mathematics

Stephen
J. Smale (1930,

Professor
Stephen J. Smale contributed greatly, in the late 50抯 and early 60抯, to the
development of differential topology, a field then in its infancy. His results
of immersions of spheres in Euclidean spaces still intrigue mathematicians, as
witnessed by recent films and pictures on his so-called 揺version?of the sphere. His proof of
the Poincaré Conjecture for dimensions bigger or
equal to 5 is one of the great mathematical achievements of the 20th Century.
His h-cobordism theorem has become probably the most
basic tool in differential geometry.

During the 60抯 Smale reshaped the view of the world of dynamical systems.
His theory of hyperbolic systems remains one of the main developments on the
subject after Poincaré, and the mathematical
foundations of the so-called 揷haos-theory?are his work as well. In the early 60抯, Smale抯 work contributed dramatically to change in the study
of the topology and analysis of infinite-dimensional manifolds. This was
achieved through his infinite-dimensional version of Morse抯 critical point
theory (known today as 揚alais-Smale Theory? and his
infinite-dimensional version of Sard抯 theorem.

In the 70抯 Smale attention turned to mechanics and economics, to which
he applied his ideas on topology and dynamics. For instance, his notion of 揳mended potential?in mechanics plays a key
role in current developments in stability and bifurcation of relative equilibria. In economics, Smale
applied an abstract theory of optimization for several functions, which he
developed, to provide conditions for the existence of Pareto optima and to
characterize this set of optima as a sub-manifold of diffeomorphic
states to the set of Pareto equilibria. He also
proved the existence of general equilibria under very
weak assumptions and contributed to the development of algorithms for the
computation of such equilibria.

It is this last
activity that led Smale in the early 80抯 to the longest
segment of his career, his work on the theory of computation and computational
mathematics. Against mainstream research on scientific computation, which
focused on immediate solutions to concrete problems, Smale
developed a theory of continuous computation and complexity (akin to that
developed by computer scientists for discrete computations), and designed and
analyzed algorithms for a number of specific problems. Some of these analyses
constitute models for the use of deep mathematics in the study of numerical
algorithms.

（转自**沃尔夫基金会官方网站**）