Finite Combinatorics, or Discrete Mathematics is a very fastly developing area in mathematics. It has many ties with Computer Science. The following branches will be emphasized: graph theory, extremal problems in combinatorics (graphs and hypergraphs), combinatorial optimization, random graphs, discrepancy theory, combinatorial number theory. On the other hand, the problems considered in Infinite Combinatorics are sometimes formally very similar to the ones in Finite Combinatorics, but the methods are closer to the methods of Set Theory. Its results are used in more theoretical areas of mathematics, like Mathematical Analysis, Topology and Set Theory. Budapest is a natural choice for a highly succesful conference in these fields because the Hungarian school is traditionally very strong in both Finite and Infinite Combinatorics; for example, the name of Paul Erdos is known all over the Globe. In addition, the organizers want to exploit that two excellent Hungarian scientists, Vera Sos and Andras Hajnal are 70 years old.
The conference will bring together top scientists and young researchers from around the world, and will certainly result in many new results in Combinatorics. This conference is actually the 11th major conference in Combinatorics in Hungary, where not only one narrow area, but most branches, that is, Combinatorics as a whole is considered. These conferences belong to the most succesful ones in the world of Combinatorics.