Hillel Furstenberg

Hillel Furstenberg, Harry Furstenberg (Hebrew הלל פורסטנברג; born September 29, 1935 in Berlin) is an Israeli mathematician who deals with probability theory, ergodic theory, topological dynamics and number theory.

Furstenberg emigrated as a child in the United States. He studied at Yeshiva University in New York, where in 1955 he received his master's degree. In 1958 he received his doctorate at Salomon Bochner at Princeton University ( Prediction Theory). In 1959 he was Moore Instructor at Massachusetts Institute of Technology. After that, he was at the University of Minnesota before he was Professor in 1965 at the Hebrew University in Jerusalem.

Furstenberg turned to methods of probability theory and ergodic theory in number theory and the theory of Lie groups. In 1955, he was with topological methods a new proof of the infinitude of primes. This conjecture was indeed already by Euclid, but were important to the methods used. In 1977, he gave a new proof of the theorem of Szemerédi ergodentheoretischen on arithmetic progressions in subsets of positive density of natural numbers, in 1972 he proved the unique ergodicity of rivers along Horozyklen on compact hyperbolic Riemann surfaces. Ergodicity for geodesic flows on compact manifolds of negative curvature has been demonstrated in the works of Gustav Hedlund and Eberhard Hopf in the late 1930s. Furstenberg is also known for its structure theorem for minimal distal flows in topological dynamics. He provided early fundamental work on random matrices (whose asymptotic behavior he sat with structural theorems on the underlying Lie groups associated ) and studied stochastic processes in homogeneous spaces and the asymptotic behavior of random walks on groups.

In 1993 he was awarded the Israel Prize and the Harvey Prize of the Technion in Haifa. In 2007 he received the Wolf Prize in Mathematics ( with Stephen Smale ). He is a member of the Israel Academy of Sciences and the National Academy of Sciences of the United States. In 2010 he gave a plenary lecture at the International Congress of Mathematicians in Hyderabad ( Ergodic structures and non Conventional ergodic theorems ), 1990 he was invited speaker at the ICM in Kyoto ( Recurrent ergodic structures and Ramsey theory ), in Stockholm in 1962 (A Poisson formula for semi - simple Lie groups) and 1970 on the ICM in Nice ( Boundaries of Lie groups and discrete subgroups ).

Among his doctoral students include Alexander Lubotzky, Vitaly Bergelson and Yuval Peres.

Writings

• On the infinitude of primes. In: American Mathematical Monthly. Vol 62, 1955, p 353
• Ergodic behavior of diagonal measures and a theorem of Szemerédi on arithmetic progressions. Journal d'Analyse Math, Vol 31, 1977, p 204-256.
• Recurrence in Ergodic Theory and Combinatorial Number Theory. Princeton University Press 1981.