A magyar nyelvû elõadás abstract-ja: An important trend in Combinatorics in recent years has been the formulation and proof of various `sparse analogues' of classical extremal results in Graph Theory and Additive Combinatorics. Due to the recent breakthroughs of Conlon and Gowers, and Schacht, many such theorems, e.g., the theorems of Turán and Erdõs and Stone in extremal graph theory, and the theorem of Szemerédi on arithmetic progressions, are now known to extend to sparse random sets. I give a survey on the recent developements. (Joint work with Robert Morris and Wojtek Samotij.)
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