József Beck
Encyclopedia
József Beck is a Harold H. Martin Professor of Mathematics at Rutgers University
.
His contributions to combinatorics include the partial colouring lemma and the Beck–Fiala theorem in discrepancy theory, the algorithmic version of the Lovász local lemma
, the two extremes theorem
in combinatorial geometry and the second moment method
in the theory of positional game
s, among others.
Beck was awarded the Fulkerson Prize
in 1985 for a paper titled "Roth's estimate of the discrepancy of integer sequences is nearly sharp", which introduced the notion of discrepancy on hypergraphs and established an upper bound on the discrepancy of the family of arithmetic progressions contained in {1,2,...,n}, matching the classical lower bound up to a polylogarithmic factor. Jiří Matoušek
and Joel Spencer
later succeeded in getting rid of this factor, showing that the bound was really sharp.
Beck gave an invited talk at the 1986 International Congress of Mathematicians
.
He is external member of the Hungarian Academy of Sciences
(2004).
Rutgers University
Rutgers, The State University of New Jersey , is the largest institution for higher education in New Jersey, United States. It was originally chartered as Queen's College in 1766. It is the eighth-oldest college in the United States and one of the nine Colonial colleges founded before the American...
.
His contributions to combinatorics include the partial colouring lemma and the Beck–Fiala theorem in discrepancy theory, the algorithmic version of the Lovász local lemma
Lovász local lemma
In probability theory, if a large number of events are all independent of one another and each has probability less than 1, then there is a positive probability that none of the events will occur...
, the two extremes theorem
Beck's theorem (geometry)
In the context of discrete geometry, Beck's theorem may refer to several different results, two of which are given below. Both appeared, alongside several other important theorems, in a well-known paper by József Beck. The two results described below primarily concern lower bounds on the number of...
in combinatorial geometry and the second moment method
Second moment method
In mathematics, the second moment method is a technique used in probability theory and analysis to show that a random variable has positive probability of being positive...
in the theory of positional game
Positional game
Positional games are a class of combinatorial games. Well-known games that fall into this class include tic-tac-toe, hex and Shannon switching game....
s, among others.
Beck was awarded the Fulkerson Prize
Fulkerson Prize
The Fulkerson Prize for outstanding papers in the area of discrete mathematics is sponsored jointly by the Mathematical Programming Society and the American Mathematical Society . Up to three awards of $1500 each are presented at each International Symposium of the MPS...
in 1985 for a paper titled "Roth's estimate of the discrepancy of integer sequences is nearly sharp", which introduced the notion of discrepancy on hypergraphs and established an upper bound on the discrepancy of the family of arithmetic progressions contained in {1,2,...,n}, matching the classical lower bound up to a polylogarithmic factor. Jiří Matoušek
Jirí Matoušek (mathematician)
Jiří Matoušek is a Czech mathematician working in computational geometry. He is a professor at Charles University in Prague and is the author of several textbooks and research monographs....
and Joel Spencer
Joel Spencer
Joel Spencer is an American mathematician. He is a combinatorialist who has worked on probabilistic methods in combinatorics and on Ramsey theory. He received his doctorate from Harvard University in 1970, under the supervision of Andrew Gleason...
later succeeded in getting rid of this factor, showing that the bound was really sharp.
Beck gave an invited talk at the 1986 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 ....
.
He is external member 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:...
(2004).
Books
- Jozsef Beck, William W. L. Chen: Irregularities of Distribution, Cambridge University Press, 1987.
- J. Beck: Combinatorial Games: Tic-Tac-Toe Theory, Cambridge University Press, 2008.
External links
- József Beck, personal webpage, Department of Mathematics, Rutgers UniversityRutgers UniversityRutgers, The State University of New Jersey , is the largest institution for higher education in New Jersey, United States. It was originally chartered as Queen's College in 1766. It is the eighth-oldest college in the United States and one of the nine Colonial colleges founded before the American...
- József Beck, Mathematics Genealogy ProjectMathematics Genealogy ProjectThe Mathematics Genealogy Project is a web-based database for the academic genealogy of mathematicians. As of September, 2010, it contained information on approximately 145,000 mathematical scientists who contribute to "research-level mathematics"...