Combinatorics is the study of existence, enumeration, and optimization of discrete configurations. A rapidly growing part of mathematics, it has applications in computer science, operation research, genetics, and other natural and social sciences. These fields in turn generate many challenging combinatorial problems. This project emphasizes the optimization or ``extremal'' aspects of combinatorics. It supports a conference on extremal combinatorial problems, entitled ``Extremal Combinatorics at Illinois'' (EXCILL), hosted by the Department of Mathematics of the University of Illinois at Urbana-Champaign on November 18-20, 2006. The organizing committee consists of J. Balogh (Secretary), Z. Furedi, S. Hartke, A. Kostochka, and D. B. West.
Topics to be discussed include extremal set theory, coloring theory for graphs and hypergraphs, Ramsey theory, cycles in graphs, discrete geometry, and probabilistic methods in combinatorics. There will be six main lectures delivered by leading experts in the field and more than 15 additional invited talks. Speakers will include senior researchers and rising stars from around the world and from a variety of backgrounds. The conference will be a major event in the Discrete Mathematics community. Participation by graduate students and young researchers will be encouraged and supported to help develop the next generation of researchers.
