Gregory Freiman

Gregory Abelevich Freiman , Russian Григорий Абелевич Фрейман (* 1926 in Kazan ) is a Russian-Israeli mathematician who deals with additive number theory and additive combinatorics. He is a professor at Tel Aviv University .

Freiman graduated from Lomonosov University in 1949, received his doctorate in 1956 from Kazan University and in 1965 at the Moscow Pedagogical Institute under Alexander Ossipowitsch Gelfond (Russian doctorate) with the thesis Structural Theory of Set Addition . He was at the University of Kazan in its branch in Elabuga (State Pedagogical Institute). In the 1970s he protested the treatment of Jewish intellectuals in the Soviet Union (published 1979 in the USA) and later immigrated to Israel.

He is known for Freiman's theorem (1964, 1966), which makes statements about a set A of natural numbers, if the sum set holds that with a constant K ( small doubling property ). After Freiman A is in a multi-dimensional arithmetic progression with inverse of K dimension and length included. New evidence comes from Imre Ruzsa (1994) and improvements to the barrier came from Tom Sanders . The theorem has also been extended to include Abelian groups, for example. ${\ displaystyle A + A}$ ${\ displaystyle | A + A | \ leq K | A |}$ ${\ displaystyle f (K) | A |}$ ${\ displaystyle f (K)}$

Fonts

Addition of finite sets, Sov. Math. Dokl. 5, 1964, 1366-1370
Foundation of a structural theory of set addition, AMS Translations of Mathematical Monographs 37, 1973 (first in Russian, Kazan 1966)
Structure theory of set addition, in Jean-Marc Deshouillers, Bernard Landreau, Alexander A. Yudin Structure Theory of Set Addition , Astérisque, SMF, Volume 258, 1999, pp. 1-33
It seems I am a Jew, Samizdat Essay on Soviet Mathematics, Southern Illinois University Press 1979 (translator Melvyn Nathanson , with appendices by Nathanson and Andrei Sakharov )

Web links

Individual evidence

↑ His name for his research field is inverse additive number theory or structure theory of sets
↑ Gregory Freiman in the Mathematics Genealogy Project (English)
↑ Shown e.g. B. in Melvyn B. Nathanson Additive Number Theory: Inverse Problems and Geometry of Sumsets , Graduate Texts in Mathematics 165, Springer Verlag 1996
↑ Ruzsa Generalized arithmetical progressions and sumsets . Acta Mathematica Hungarica 65, 1995, 379-388

personal data
SURNAME	Freiman, Gregory
ALTERNATIVE NAMES	Freiman, Gregory Abelevich
BRIEF DESCRIPTION	Israeli mathematician
DATE OF BIRTH	1926
PLACE OF BIRTH	Kazan

[1] His name for his research field is inverse additive number theory or structure theory of sets

[2] Gregory Freiman in the Mathematics Genealogy Project (English)

[3] Shown e.g. B. in Melvyn B. Nathanson Additive Number Theory: Inverse Problems and Geometry of Sumsets , Graduate Texts in Mathematics 165, Springer Verlag 1996

[4] Ruzsa Generalized arithmetical progressions and sumsets . Acta Mathematica Hungarica 65, 1995, 379-388