Zoltán Füredi (

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 Carpathian Basin, it is bordered by Slovakia to the north, Ukraine to the northeast, Romania to the east and southeast, Serbia to the south, Croatia a ...

, 21 May 1954) is a Hungarian mathematician, working in

combinatorics Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many appl ...

, mainly in

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 geome ...

and

extremal combinatorics Extremal combinatorics is a field of combinatorics, which is itself a part of mathematics. Extremal combinatorics studies how large or how small a collection of finite objects (numbers, graphs, vectors, sets, etc.) can be, if it has to satisfy ce ...

. He was a student of

Gyula O. H. Katona Gyula O. H. Katona (born 16 March 1941 in Budapest) is a Hungarian mathematician known for his work in combinatorial set theory, and especially for the Kruskal–Katona theorem In algebraic combinatorics, the Kruskal–Katona theorem gives a co ...

. He is a corresponding member of the

Hungarian Academy of Sciences The Hungarian Academy of Sciences ( hu, Magyar Tudományos Akadémia, MTA) is the most important and prestigious learned society of Hungary. Its seat is at the bank of the Danube in Budapest, between Széchenyi rakpart and Akadémia utca. Its ma ...

(2004). He is a research professor of the Rényi Mathematical Institute of the Hungarian Academy of Sciences, and a professor at the

University of Illinois Urbana-Champaign The University of Illinois Urbana-Champaign (U of I, Illinois, University of Illinois, or UIUC) is a public land-grant research university in Illinois in the twin cities of Champaign and Urbana. It is the flagship institution of the University ...

(UIUC). Füredi received his

Candidate of Sciences Candidate of Sciences (russian: кандидат наук, translit=kandidat nauk) is the first of two doctoral level scientific degrees in Russia and the Commonwealth of Independent States. It is formally classified as UNESCO's ISCED level 8, "do ...

degree in mathematics in 1981 from the Hungarian Academy of Sciences.

Some results

* In infinitely many cases he determined the maximum number of edges in a

graph Graph may refer to: Mathematics *Graph (discrete mathematics), a structure made of vertices and edges **Graph theory, the study of such graphs and their properties *Graph (topology), a topological space resembling a graph in the sense of discre ...

with no ''C''₄. * With

Paul Erdős Paul Erdős ( hu, Erdős Pál ; 26 March 1913 – 20 September 1996) was a Hungarian mathematician. He was one of the most prolific mathematicians and producers of mathematical conjectures of the 20th century. pursued and proposed problems in ...

he proved that for some ''c''>1, there are ''c''^''d'' points in ''d''-dimensional space such that all triangles formed from those points are

acute Acute may refer to: Science and technology * Acute angle ** Acute triangle ** Acute, a leaf shape in the glossary of leaf morphology * Acute (medicine), a disease that it is of short duration and of recent onset. ** Acute toxicity, the adverse eff ...

. * With

Imre Bárány Imre Bárány (Mátyásföld, Budapest, 7 December 1947) 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 app ...

he proved that no

polynomial time In computer science, the time complexity is the computational complexity that describes the amount of computer time it takes to run an algorithm. Time complexity is commonly estimated by counting the number of elementary operations performed by ...

algorithm determines the volume of

convex bodies In mathematics, a convex body in n-dimensional Euclidean space \R^n 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; that is to say, a point x lies in ...

in dimension ''d'' within a multiplicative error ''d''^''d''. * He proved that there are at most

O(n\log n)

unit distances in a convex ''n''-gon. * In a paper written with coauthors he solved the Hungarian

lottery A lottery is a form of gambling that involves the drawing of numbers at random for a prize. Some governments outlaw lotteries, while others endorse it to the extent of organizing a national or state lottery. It is common to find some degree of ...

problem. * With

Ilona Palásti Ilona Palásti (1924–1991) was a Hungarian mathematician who worked at the Alfréd Rényi Institute of Mathematics. She is known for her research in discrete geometry, geometric probability, and the theory of random graphs. With Alfréd Rényi a ...

he found the best known lower bounds on the

orchard-planting problem In discrete geometry, the original orchard-planting problem asks for the maximum number of 3-point lines attainable by a configuration of a specific number of points in the plane. It is also called the tree-planting problem or simply the orchard ...

of finding sets of points with many 3-point lines. * He proved an upper bound on the ratio between the fractional matching number and the matching number in a hypergraph.

References

External links

Füredi's UIUC home page
20th-century Hungarian mathematicians 21st-century Hungarian mathematicians Members of the Hungarian Academy of Sciences Combinatorialists University of Illinois Urbana-Champaign faculty 1954 births Living people {{Europe-mathematician-stub