Imre Bárány
Encyclopedia
Imre Bárány is a Hungarian mathematician
, working in combinatorics
and discrete geometry
. He works at the Rényi Mathematical Institute
of the Hungarian Academy of Sciences
, and has a part-time job at the University College London
.
) of the Hungarian Academy of Sciences
in 1985. He was an invited speaker at the Combinatorics session of the International Congress of Mathematicians
, in Beijing
, 2002. He was elected a corresponding member of the Hungarian Academy of Sciences (2010).
He is an Editorial Board member for the journals Combinatorica
, Mathematika, and the Online Journal of Analytic Combinatorics".
He is area editor of the journal Mathematics of Operations Research
.
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
, working in combinatorics
Combinatorics
Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures. Aspects of combinatorics include counting the structures of a given kind and size , deciding when certain criteria can be met, and constructing and analyzing objects meeting the criteria ,...
and discrete geometry
Discrete geometry
Discrete geometry and combinatorial geometry are branches of geometry that study combinatorial properties and constructive methods of discrete geometric objects. Most questions in discrete geometry involve finite or discrete sets of basic geometric objects, such as points, lines, planes, circles,...
. He works at the Rényi Mathematical Institute
Alfréd Rényi Institute of Mathematics
The Alfréd Rényi Institute of Mathematics is the research institute in mathematics of the Hungarian Academy of Sciences. It was created in 1950 by Alfréd Rényi, who directed it until his death. Since its creation, the institute has been the center of mathematical research in Hungary. It received...
of the Hungarian Academy of Sciences
Hungarian Academy of Sciences
The Hungarian Academy of Sciences is the most important and prestigious learned society of Hungary. Its seat is at the bank of the Danube in Budapest.-History:...
, and has a part-time job at the University College London
University College London
University College London is a public research university located in London, United Kingdom and the oldest and largest constituent college of the federal University of London...
.
Notable results
- He gave a surprisingly simple alternative proof of LovászLászló LovászLászló Lovász is a Hungarian mathematician, best known for his work in combinatorics, for which he was awarded the Wolf Prize and the Knuth Prize in 1999, and the Kyoto Prize in 2010....
's theorem on Kneser graphKneser graphIn graph theory, the Kneser graph is the graph whose vertices correspond to the -element subsets of a set of elements, and where two vertices are connected if and only if the two corresponding sets are disjoint...
s. - He gave a new proof to the Borsuk–Ulam theoremBorsuk–Ulam theoremIn mathematics, the Borsuk–Ulam theorem, named after Stanisław Ulam and Karol Borsuk, states that every continuous function from an n-sphere into Euclidean n-space maps some pair of antipodal points to the same point....
. - Barany gave a colored version of Carathéodory's theoremCarathéodory's theorem (convex hull)In convex geometry Carathéodory's theorem states that if a point x of Rd lies in the convex hull of a set P, there is a subset P′ of P consisting of d+1 or fewer points such that x lies in the convex hull of P′. Equivalently, x lies in an r-simplex with vertices in P, where r \leq d...
. - He solved an old problem of SylvesterJames Joseph SylvesterJames Joseph Sylvester was an English mathematician. He made fundamental contributions to matrix theory, invariant theory, number theory, partition theory and combinatorics...
on the probability of random point sets in convex position. - With VuVan H. VuVan H. Vu is a Vietnamese mathematician, a professor of mathematics at Yale University and the 2008 winner of the Pólya Prize of the Society for Industrial and Applied Mathematics for his work on concentration of measure. He is a collaborator of Terence Tao....
proved a central limit theoremCentral limit theoremIn probability theory, the central limit theorem states conditions under which the mean of a sufficiently large number of independent random variables, each with finite mean and variance, will be approximately normally distributed. The central limit theorem has a number of variants. In its common...
on random points in convex bodiesConvex bodyIn mathematics, a convex body in n-dimensional Euclidean space Rn is a compact convex set with non-empty interior.A convex body K is called symmetric if it is centrally symmetric with respect to the origin, i.e. a point x lies in K if and only if its antipode, −x, also lies in K...
. - With FürediZoltán FürediZoltán Füredi is a Hungarian mathematician, working in combinatorics, mainly in discrete geometry and extremal combinatorics. He was a student of Gyula O. H. Katona. He is a corresponding member of the Hungarian Academy of Sciences...
he gave an algorithm for mental pokerMental pokerMental poker is the common name for a set of cryptographic problems that concerns playing a fair game over distance without the need for a trusted third party. The term is also applied to the theories surrounding these problems and their possible solutions. The name stems from the card game poker...
. - With FürediZoltán FürediZoltán Füredi is a Hungarian mathematician, working in combinatorics, mainly in discrete geometry and extremal combinatorics. He was a student of Gyula O. H. Katona. He is a corresponding member of the Hungarian Academy of Sciences...
he proved that no deterministic polynomial time algorithm determines the volume of convex bodies in dimension d within a multiplicative error dd. - With FürediZoltán FürediZoltán Füredi is a Hungarian mathematician, working in combinatorics, mainly in discrete geometry and extremal combinatorics. He was a student of Gyula O. H. Katona. He is a corresponding member of the Hungarian Academy of Sciences...
and PachJános PachJános Pach is a mathematician and computer scientist working in the fields of combinatorics and discrete and computational geometry...
he proved the following six circle conjecture of Fejes TóthLászló Fejes TóthLászló Fejes Tóth was a Hungarian mathematician who specialised in geometry. He proved that a honeycomb pattern is the most efficient way to pack centrally symmetric convex sets on the Euclidean plane . He also investigated packings on the sphere...
: if in a planar circle packingCircle packingIn geometry, circle packing is the study of the arrangement of circles on a given surface such that no overlapping occurs and so that all circles touch another. The associated "packing density", η of an arrangement is the proportion of the surface covered by the circles...
each circle is tangent to at least 6 other circles, then either it is the hexagonal system of circles with identical radii, or there are circles with arbitrarily small radius.
Career
Bárány received the Mathematical Prize (now Paul Erdős PrizePaul Erdős Prize
The Paul Erdős Prize is given to Hungarian mathematicians not older than 40 by the Mathematics Department of the Hungarian Academy of Sciences...
) of the Hungarian Academy of Sciences
Hungarian Academy of Sciences
The Hungarian Academy of Sciences is the most important and prestigious learned society of Hungary. Its seat is at the bank of the Danube in Budapest.-History:...
in 1985. He was an invited speaker at the Combinatorics session of the International Congress of Mathematicians
International Congress of Mathematicians
The International Congress of Mathematicians is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union ....
, in Beijing
Beijing
Beijing , also known as Peking , is the capital of the People's Republic of China and one of the most populous cities in the world, with a population of 19,612,368 as of 2010. The city is the country's political, cultural, and educational center, and home to the headquarters for most of China's...
, 2002. He was elected a corresponding member of the Hungarian Academy of Sciences (2010).
He is an Editorial Board member for the journals Combinatorica
Combinatorica
Combinatorica is an international journal of mathematics, publishing papers in the fields of combinatorics and computer science. It started in 1981, with László Babai and László Lovász as the editors-in-chief with Paul Erdős as honorary editor-in-chief. The current editors-in-chief are László...
, Mathematika, and the Online Journal of Analytic Combinatorics".
He is area editor of the journal Mathematics of Operations Research
Mathematics of Operations Research
Mathematics of Operations Research is a scholarly journal published since 1976. The founding editor was Arthur F. Veinott, Jr. of Stanford University, who served as editor-in-chief 1976-1980. MOR is published quarterly by INFORMS and indexed by Journal Citation Reports...
.
External links
- Personal webpage, Mathematical Institute of the Hungarian Academy of SciencesHungarian Academy of SciencesThe Hungarian Academy of Sciences is the most important and prestigious learned society of Hungary. Its seat is at the bank of the Danube in Budapest.-History:...
- Personal webpage, Department of Mathematics, University College LondonUniversity College LondonUniversity College London is a public research university located in London, United Kingdom and the oldest and largest constituent college of the federal University of London...