Hillel Furstenberg
Encyclopedia
Hillel Fürstenberg (born September 29, 1935) is an American-Israeli mathematician
, a member of the Israel Academy of Sciences and Humanities
and U.S. National Academy of Sciences and a laureate of the Wolf Prize in Mathematics
. He is known for his application of probability theory
and ergodic theory
methods to other areas of mathematics, including number theory
and Lie group
s. He gained attention at an early stage in his career for producing an innovative topological proof of the infinitude of prime numbers
. He proved unique ergodicity of horocycle flows on a compact hyperbolic Riemann surface
s in the early 1970s. In 1977, he gave an ergodic theory reformulation, and subsequently proof, of Szemerédi's theorem
. The Fürstenberg boundary and Fürstenberg compactification of a locally symmetric space are named after him.
, in 1935, and the family emigrated to the United States
in 1939, shortly before the outbreak of the Second World War. In the Yeshiva University
he concluded his BA and MSc studies in 1955. He obtained his Ph. D. under Salomon Bochner
at Princeton University
in 1958. After several years at the University of Minnesota
he became a Professor of Mathematics at the Hebrew University of Jerusalem
in 1965.
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
, a member of the Israel Academy of Sciences and Humanities
Israel Academy of Sciences and Humanities
The Israel Academy of Sciences and Humanities, based in Jerusalem, was set up in 1961 by the State of Israel to foster contact between scholars from the sciences and humanities in Israel, to advise the government on research projects of national importance, and to promote excellence. It comprises...
and U.S. National Academy of Sciences and a laureate of the Wolf Prize in Mathematics
Wolf Prize in Mathematics
The Wolf Prize in Mathematics is awarded almost annually by the Wolf Foundation in Israel. It is one of the six Wolf Prizes established by the Foundation and awarded since 1978; the others are in Agriculture, Chemistry, Medicine, Physics and Arts...
. He is known for his application of probability theory
Probability theory
Probability theory is the branch of mathematics concerned with analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single...
and ergodic theory
Ergodic theory
Ergodic theory is a branch of mathematics that studies dynamical systems with an invariant measure and related problems. Its initial development was motivated by problems of statistical physics....
methods to other areas of mathematics, including number theory
Number theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...
and Lie group
Lie group
In mathematics, a Lie group is a group which is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure...
s. He gained attention at an early stage in his career for producing an innovative topological proof of the infinitude of prime numbers
Furstenberg's proof of the infinitude of primes
In number theory, Hillel Fürstenberg's proof of the infinitude of primes is a celebrated topological proof that the integers contain infinitely many prime numbers. When examined closely, the proof is less a statement about topology than a statement about certain properties of arithmetic sequences....
. He proved unique ergodicity of horocycle flows on a compact hyperbolic Riemann surface
Riemann surface
In mathematics, particularly in complex analysis, a Riemann surface, first studied by and named after Bernhard Riemann, is a one-dimensional complex manifold. Riemann surfaces can be thought of as "deformed versions" of the complex plane: locally near every point they look like patches of the...
s in the early 1970s. In 1977, he gave an ergodic theory reformulation, and subsequently proof, of Szemerédi's theorem
Szemerédi's theorem
In number theory, Szemerédi's theorem is a result that was formerly the Erdős–Turán conjecture...
. The Fürstenberg boundary and Fürstenberg compactification of a locally symmetric space are named after him.
Biography
Hillel Fürstenberg was born in GermanyGermany
Germany , officially the Federal Republic of Germany , is a federal parliamentary republic in Europe. The country consists of 16 states while the capital and largest city is Berlin. Germany covers an area of 357,021 km2 and has a largely temperate seasonal climate...
, in 1935, and the family emigrated to the United States
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
in 1939, shortly before the outbreak of the Second World War. In the Yeshiva University
Yeshiva University
Yeshiva University is a private university in New York City, with six campuses in New York and one in Israel. Founded in 1886, it is a research university ranked as 45th in the US among national universities by U.S. News & World Report in 2012...
he concluded his BA and MSc studies in 1955. He obtained his Ph. D. under Salomon Bochner
Salomon Bochner
Salomon Bochner was an American mathematician of Austrian-Hungarian origin, known for wide-ranging work in mathematical analysis, probability theory and differential geometry.- Life :...
at Princeton University
Princeton University
Princeton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League, and is one of the nine Colonial Colleges founded before the American Revolution....
in 1958. After several years at the University of Minnesota
University of Minnesota
The University of Minnesota, Twin Cities is a public research university located in Minneapolis and St. Paul, Minnesota, United States. It is the oldest and largest part of the University of Minnesota system and has the fourth-largest main campus student body in the United States, with 52,557...
he became a Professor of Mathematics at the Hebrew University of Jerusalem
Hebrew University of Jerusalem
The Hebrew University of Jerusalem ; ; abbreviated HUJI) is Israel's second-oldest university, after the Technion – Israel Institute of Technology. The Hebrew University has three campuses in Jerusalem and one in Rehovot. The world's largest Jewish studies library is located on its Edmond J...
in 1965.
Awards
- 1993 – Fürstenberg received the Israel PrizeIsrael PrizeThe Israel Prize is an award handed out by the State of Israel and is largely regarded as the state's highest honor. It is presented annually, on Israeli Independence Day, in a state ceremony in Jerusalem, in the presence of the President, the Prime Minister, the Knesset chairperson, and the...
, for exact sciences. - 1993 – Fürstenberg received the Harvey Prize from Technion.
- 2006/7 – He received the Wolf Prize in MathematicsWolf Prize in MathematicsThe Wolf Prize in Mathematics is awarded almost annually by the Wolf Foundation in Israel. It is one of the six Wolf Prizes established by the Foundation and awarded since 1978; the others are in Agriculture, Chemistry, Medicine, Physics and Arts...
.
External links
See also
- Compactification (mathematics)Compactification (mathematics)In mathematics, compactification is the process or result of making a topological space compact. The methods of compactification are various, but each is a way of controlling points from "going off to infinity" by in some way adding "points at infinity" or preventing such an "escape".-An...
- Ratner's theoremsRatner's theoremsIn mathematics, Ratner's theorems are a group of major theorems in ergodic theory concerning unipotent flows on homogeneous spaces proved by Marina Ratner around 1990. The theorems grew out of Ratner's earlier work on horocycle flows. The study of the dynamics of unipotent flows played a decisive...
- List of Israel Prize recipients