Local-vs-global combinatorics

  • Asaf Shapira

    School of Mathematical Sciences, Tel Aviv University, Tel Aviv, 6997801, Israel
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Many of the most outstanding open problems in combinatorics relate the local and global properties of large discrete structures. The research aimed at solving these questions led to some of the most important developments in this area, as well as in related areas such as theoretical computer science, additive number theory, and harmonic analysis. In this paper we discuss some of these advances and mention several open problems.