József Beck (

Budapest Budapest (, ; ) is the capital and most populous city of Hungary. It is the ninth-largest city in the European Union by population within city limits and the second-largest city on the Danube river; the city has an estimated population ...

Hungary Hungary ( hu, Magyarország ) is a landlocked country in Central Europe. Spanning of the Pannonian Basin, Carpathian Basin, it is bordered by Slovakia to the north, Ukraine to the northeast, Romania to the east and southeast, Serbia to the ...

, February 14, 1952) is a Harold H. Martin Professor of Mathematics at

Rutgers University Rutgers University (; RU), officially Rutgers, The State University of New Jersey, is a public land-grant research university consisting of four campuses in New Jersey. Chartered in 1766, Rutgers was originally called Queen's College, and was ...

. 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 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 geo ...

and the second moment method in the theory of

positional game A positional game is a kind of a combinatorial game for two players. It is described by: *Xa finite set of elements. Often ''X'' is called the ''board'' and its elements are called ''positions''. *\mathcala family of subsets of X. These subset ...

s, among others. Beck was awarded the

Fulkerson Prize The Fulkerson Prize for outstanding papers in the area of discrete mathematics is sponsored jointly by the Mathematical Optimization Society (MOS) and the American Mathematical Society (AMS). Up to three awards of $1,500 each are presented at e ...

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

hypergraph In mathematics, a hypergraph is a generalization of a graph in which an edge can join any number of vertices. In contrast, in an ordinary graph, an edge connects exactly two vertices. Formally, an undirected hypergraph H is a pair H = (X,E) w ...

s and established an upper bound on the discrepancy of the family of arithmetic progressions contained in , matching the classical lower bound up to a polylogarithmic factor. Jiří Matoušek and

Joel Spencer Joel Spencer (born April 20, 1946) is an American mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, da ...

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 an external member of the Hungarian Academy of Sciences (2004).

Books

*''Irregularities of Distribution'' (with William W. L. Chen, Cambridge Tracts in Mathematics 89, Cambridge University Press, 1987) *'' Combinatorial Games: Tic-Tac-Toe Theory'' (Encyclopedia of Mathematics and its Applications 114, Cambridge University Press, 2008) *''Inevitable Randomness in Discrete Mathematics (University Lecture Series 49, American Mathematical Society, 2009)'' *''Probabilistic Diophantine Approximation: Randomness in Lattice Point Counting'' (Springer Monographs in Mathematics. Springer-Verlag, 2014) *''Strong Uniformity and Large Dynamical Systems'' (World Scientific Publishing, 2018)

References

External links

József Beck, personal webpage
Department of Mathematics,

József Beck

Mathematics Genealogy Project The Mathematics Genealogy Project (MGP) is a web-based database for the academic genealogy of mathematicians.. By 31 December 2021, it contained information on 274,575 mathematical scientists who contributed to research-level mathematics. For a ty ...

Mathematicians from Budapest Members of the Hungarian Academy of Sciences 1952 births Living people Rutgers University faculty Positional games Hungarian emigrants to the United States {{Europe-mathematician-stub