## Zoltan Furedi

### Combinatorics

Professor Füredi’s interest includes “everything which is finite”. His main field is the theory of finite sets with applications in geometry, designs, and computer science. This rapidly developing field is extremely problem oriented. However, the topic is not simply a collection of problems. Finite mathematics (Combinatorics) applies a broad array of tools and results from other topics like number theory, linear and commutative algebra, probability theory, geometry, and information theory. On the other hand, it has a number of interesting applications in all parts of geometry, integer programming, and computer science. Few notions are as simple in mathematics as that of a family of finite sets, or in other words, a hypergraph. This simplicity lends to them a vast versatility in applications. As one of the greatest mathematicians of this century, I. M. Gelfand, said, “The older I get, the more I believe that at the bottom of most deep questions in mathematics, there is a combinatorial problem.” He has studied how local properties affect the global parameters of different combinatorial structures and proposes to continue this research to find more geometric representations, where Turan numbers naturally emerge. He is internationally recognized as a leading expert in the field of extremal combinatorics. He serves on the editorial board of eight professional journals, and has published over 170 papers. His extended survey provides a unique comprehensive summary of the matching theory of hypergraphs. He is frequently invited as a principal speaker to international conferences (the British Combinatorial meeting, 1990; ICM, 1994, Zurich; Canadian Winter Meeting, 1998). He has developed valuable techniques and has shown deep insight, particularly in extremal problems. His series of applications of the Delta-system method, a method discovered by Erdos and Rado (1960) and developed by Deza, Frankl and Füredi to handle Turan-type questions, includes a solution of Erdos’ one-forbidden-intersection conjecture (1988). This result was recognized by the R’enyi prize, awarded the best theorem of the year in Hungary.