Imre Ruzsa

Imre Z. Ruzsa (born July 23, 1953 in Budapest ) is a Hungarian mathematician who deals with combinatorics, number theory and probability theory.

Ruzsa won a silver medal in 1969 and gold medals (with top scores) in 1970 and 1971 at the International Mathematical Olympiad. He studied at the Lorand Eötvös University in Budapest, graduating in 1976. He then went to the Alfred Renyi Institute of the Hungarian Academy of Sciences.

In 1987 he proved a theorem about the minimum number of elements in essential components , a concept of additive number theory that comes from Alexander Chintschin and denotes sets of natural numbers that add these densities to sets with Schnirelmann densities (according to Lew Genrichowitsch Schnirelman ) between 0 and 1 increase. According to Ruzsa's theorem, essential components have at least elements less than or equal to x with (he also proved that for each there is an essential component with these properties). ${\ displaystyle {\ log (x)} ^ {c}}$ ${\ displaystyle c> 1}$ ${\ displaystyle c> 1}$

In 1994 he gave a new proof of Gregory Freiman's theorem in additive number theory.

In 1988 he received the Rollo Davidson Prize . He was invited speaker at the International Congress of Mathematicians in Madrid 2006 (Additive Combinatorics and Geometry of Numbers) and at the European Congress of Mathematicians in Stockholm 2004. He is a Fellow of the American Mathematical Society .

His father Imre Ruzsa was also a mathematician.

Fonts

with Endre Szemerédi : Triple systems with no six points carrying three triangles. Colloq. Math. Soc. János Bolyai, Volume 18, North-Holland, Amsterdam-New York 1978, pp. 939-945.
Essential components. Proceedings of the London Mathematical Society, Volume 54, 1987, pp. 38-56.
Generalized arithmetical progressions and sumsets. Acta Mathematica Hungarica, Volume 65 1994, pp. 379-388 (Freiman's theorem)
The Brunn-Minkowski inequality and nonconvex sets. Geometriae Dedicata, Volume 67, 1997, pp. 337-348
with Gábor J. Székely : Algebraic Probability Theory , Wiley, 1988

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personal data
SURNAME	Ruzsa, Imre
ALTERNATIVE NAMES	Ruzsa, Imre Z.
BRIEF DESCRIPTION	Hungarian mathematician
DATE OF BIRTH	July 23, 1953
PLACE OF BIRTH	Budapest