"Combinatorics is one of the most active research areas in pure mathematics today. It has close ties and applications to many other fields, such as geometry, number theory, statistical physics and computer science. New concepts and tools have been introduced, some old problems have been solved, and a plethora of challenging new questions have emerged. It has attracted a considerable amount of attention from many of the world's leading mathematicians, as demonstrated by the Wolf Prize in 1983 and 1999, by the Fields Medal in 1998 and 2006 and by the Abel Prize in 2012.One of the most important trends in combinatorics has been studying various random analogues of well-known theorems in extremal graph theory, Ramsey theory and additive combinatorics. Despite recent progress, many important questions have remained open, Balogh proposes to address several of them. It is also expected that this project leads to new exciting questions and directions.Balogh's secondary goal is to further develop his collaboration with some of the researchers from the host institution and other European researchers, which has the potential of becoming a life-long collaboration. It would also establish new collaborative links worldwide; such as creating connections between the host institute and other highly regarded research groups.Balogh is an expert on most aspects of combinatorics: graph theory, probabilistic methods, random graphs, bootstrap percolation. After more than a decade of successful research in the US, he would like to return to Europe at least for a year. The University of Szeged is an excellent host institution with a great history accommodating many talented researchers as well as students, thus, Balogh could ease the continuity of up-to-date research while there.The project would raise the status of the European Research Area. In particular it would have a long-lasting impact on the host insitute by introducing them to the latest trends in modern combinatorics."