Hillel Furstenberg
Harry Furstenberg | |
---|---|
Awards | Abel Prize Israel Prize Harvey Prize Wolf Prize |
Scientific career | |
Fields | Mathematics |
Thesis | Prediction Theory (1958) |
Doctoral advisor | Salomon Bochner |
Doctoral students | Alexander Lubotzky Vitaly Bergelson Shahar Mozes Yuval Peres Tamar Ziegler |
Hillel "Harry" Furstenberg (
Biography
Furstenberg was born to
Academic career
Furstenberg pursued his doctorate at Princeton University under the supervision of Salomon Bochner. In 1958 he received his PhD for his thesis, Prediction Theory.[2]
From 1959–1960, Furstenberg served as the C. L. E. Moore instructor at the Massachusetts Institute of Technology.[3]
Furstenberg got his first job as an assistant professor in 1961 at the
In 2003, Hebrew University and
In 1993, Furstenberg won the Israel Prize and in 2007, the Wolf Prize in mathematics. He is a member of the
Fustenberg has taught generations of students, including Alexander Lubotzky, Yuval Peres, Tamar Ziegler, Shahar Mozes, and Vitaly Bergelson.[9]
Research accomplishments
Furstenberg gained attention at an early stage in his career for producing an innovative topological proof of the infinitude of prime numbers in 1955.
In a series of articles beginning in 1963 with A Poisson Formula for Semi-Simple
In his 1967 paper, Disjointness in ergodic theory, minimal sets, and a problem in Diophantine approximation, Furstenberg introduced the notion of 'disjointness,' a notion in ergodic systems that is analogous to coprimality for integers. The notion turned out to have applications in areas such as number theory, fractals, signal processing and electrical engineering.
In 1977, he gave an ergodic theory reformulation, and subsequently proof, of Szemerédi's theorem. This is described in his 1977 paper, Ergodic behavior of diagonal measures and a theorem of Szemerédi on arithmetic progressions. Furstenberg used methods from ergodic theory to prove a celebrated result by Endre Szemerédi, which states that any subset of integers with positive upper density contains arbitrarily large arithmetic progressions. His insights then led to later important results, such as the proof by Ben Green and Terence Tao that the sequence of prime numbers includes arbitrary large arithmetic progressions.
He proved unique ergodicity of horocycle flows on compact hyperbolic
Personal life
In 1958, Furstenberg married Rochelle (née) Cohen, a journalist and literary critic. Together they have five children and sixteen grandchildren.[4]
Awards
- 1977 – Rothschild Prize in Mathematics.[10]
- 1993 – Furstenberg received the Israel Prize, for exact sciences.[11]
- 1993 – Furstenberg received the Harvey Prize from Technion.[12]
- 2006/7 – He received the Wolf Prize in Mathematics.[13]
- 2006 – He delivered the Paul Turán Memorial Lectures.[14]
- 2020 – He received the Gregory Margulis "for pioneering the use of methods from probability and dynamics in group theory, number theory and combinatorics".[15]
Selected publications
- Furstenberg, Harry, Stationary processes and prediction theory, Princeton, N.J., Princeton University Press, 1960.[16][17]
- Furstenberg, Harry (March 1963). "A Poisson Formula for Semi-Simple Lie Groups". Annals of Mathematics. Second Series. 77 (2): 335–386. JSTOR 1970220.
- Furstenberg, Harry (1967). "Disjointness in ergodic theory, minimal sets, and a problem in diophantine approximation". Mathematical Systems Theory. 1: 1–49. S2CID 206801948.
- Furstenberg, Harry (1977). "Ergodic behavior of diagonal measures and a theorem of Szemerédi on arithmetic progressions". S2CID 120917478.
- Furstenberg, Harry, Recurrence in ergodic theory and combinatorial number theory, Princeton, N.J., Princeton Univ. Press, 1981.[18][19]
See also
References
- ^ Chang, Kenneth. "Abel Prize in Mathematics Shared by 2 Trailblazers of Probability and Dynamics Hillel Furstenberg, 84, and Gregory Margulis, 74, both retired professors, share the mathematics equivalent of a Nobel Prize." Archived March 18, 2020, at the Wayback Machine, The New York Times, March 18, 2020. Accessed March 18, 2020. "Dr. Furstenberg was born in Berlin in 1935. His family, which was Jewish, was able to leave Germany just before the start of World War II and made its way to the United States, settling in New York City in the Washington Heights neighborhood in Manhattan."
- ^ MacTutor History of Mathematics archive. Retrieved March 22, 2020.
- New York Times. Retrieved March 22, 2020.
- ^ The Abel Prize. Retrieved March 22, 2020.
- Ben-Gurion University. Retrieved March 22, 2020.
- ^ "Prof. Hillel Furstenberg". Israel Academy of Sciences and Humanities. Retrieved March 22, 2020.
- ^ "Dr Hillel Furstenberg". American Academy of Arts and Sciences. Retrieved March 22, 2020.
- U.S. National Academy of Sciences. Retrieved March 22, 2020.
- ^ "Harry Furstenberg – The Mathematics Genealogy Project". www.genealogy.math.ndsu.nodak.edu. Retrieved March 19, 2020.
- ^ "The Rothschild Prize". Yad Hanadiv. Retrieved July 19, 2020.
- ^ "Israel Prize Official Site – Recipients in 1993 (in Hebrew)". Archived from the original on October 12, 2014.
- ^ "Prize Winners – Harvey Prize". Technion – Israel Institute of Technology. Retrieved March 22, 2020.
- ^ "Furstenberg and Smale Receive 2006–2007 Wolf Prize" (PDF). Notices of the American Mathematical Society. 54 (4): 631–632. 2007.
- ^ "Turán Memorial Lectures". Archived from the original on September 21, 2019. Retrieved September 14, 2019.
- from the original on March 18, 2020. Retrieved March 18, 2020.
- ISBN 0691080410.
- from the original on May 17, 2014. Retrieved September 24, 2012.
- ISBN 9780691082691.
- from the original on May 17, 2014. Retrieved September 24, 2012.