Imre Bárány

Imre Bárány ( born December 7, 1947 in Mátyásföld, Budapest) is a Hungarian mathematician who deals with combinatorics and discrete geometry.

Bárány is a mathematician at the Alfred Renyi Institute of the Hungarian Academy of Sciences. He is also a professor at University College London.

In 1978, he gave a new, short proof of the conjecture of Martin Kneser on the chromatic number of Kneser graphs. In 1980, he gave a new proof of the theorem of Borsuk and Ulam. In 1981 he proved with SB Shlosman and A. Szucs a topological generalization of a set of Helge Tverberg (see Topological combinatorics ).

With Zoltán Füredi, he gave an algorithm for the cryptographic protocol Mental Poker and proved that the calculation of the volume of an area defined by one Membership oracle for points convex set in d- dimensional space is a generally difficult ( non- polynomial -temporal ) problem.

In 2000, he solved the problem of James Joseph Sylvester on the probability that randomly distributed points are in convex position. Sylvester asked originally in 1864, according to the probability that four randomly chosen points in the plane form a convex quadrilateral not. The generalization asks for the probability p ( K, n) that n randomly chosen points of a convex polytope K are in d dimensions in convex position, that is not a point of n randomly chosen points lies in the convex hull of the other. Barany dealt with several cases of the generalized problem.

With Vershik and Pach he solved a problem of Vladimir Arnold on the number of convex polytopes of grid points. With Van Vu, he proved a central limit theorem for random polytopes ..

In 1989 he proved with László Lovász and Füredi an asymptotic estimate for the number of levels that share a set S of n points in three-dimensional Euclidean space in general position in two halves ( the planes go each by three points of S). With Füredi and J. Pach he proved the six -circle conjecture of László Fejes Tóth. It states that occur in a circle packing in the plane in which each circle has six neighboring counties, either the hexagonal circle packing with circles of equal radius is present or circles with arbitrary small radius.

In 1985 he received the mathematics prize of the Hungarian Academy of Sciences and in 2010 he became its corresponding member. In 2002 he was invited speaker at the International Congress of Mathematicians in Beijing (random points, convex bodies, and lattices ). He is a Fellow of the American Mathematical Society.