# Hillel (Harry) Furstenberg

Wolf Prize Laureate in Mathematics 2006/7

**Hillel (Harry) Furstenberg**

#### Affiliation at the time of the award:

**The Hebrew University of Jerusalem****, Israel**

#### Award citation:

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

#### Prize share:

**Harry Furstenberg **

**Stephen Smale**

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’s 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.