Imre Z Ruzsa

Imre Z. Ruzsa (born 23 July 1953) is a Hungarian mathematician specializing in number theory.

Ruzsa participated in the International Mathematical Olympiad for Hungary, winning a silver medal in 1969, and two consecutive gold medals with perfect scores in 1970 and 1971. He graduated from the Eotvos Lorand University in 1976. Since then he has been at the Alfred Renyi Institute of Mathematics of the Hungarian Academy of Sciences. He was awarded the Rollo Davidson Prize in 1988. He was elected corresponding member (1998) and member (2004) of the Hungarian Academy of Sciences. He was invited speaker at the European Congress of Mathematics at Stockholm, 2004, and in the Combinatorics section of the International Congress of Mathematicians in Madrid, 2006. In 2012 he became a fellow of the American Mathematical Society.

With Endre Szemeredi he proved that on n points only o(n²) triples can be given such that the union of any 3 of them contains at least 7 points. He proved that an essential component has at least (log x)^1+ε elements up to x, for some ε > 0. On the other hand, for every ε > 0 there is an essential component that has at most (log x)^1+ε elements up to x, for every x. He gave a new proof to Freiman's theorem. Ruzsa also showed the existence of a Sidon sequence which has at least x^0.41 elements up to x.

In a result complementing the Erdos–Fuchs theorem he showed that there exists a sequence a₀, a₁, ... of natural numbers such that for every n the number of solutions of the inequality a_i + a_j ≤ n is cn + O(n^1/4log n) for some c > 0.