Extremal and Probabilistic Combinatorics II

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The investigators continue their work on graph drawing and crossing numbers, random graph models, phylogeny reconstruction, and on fundamental questions of extremal set and graph theory and discrete geometry. In particular, they will focus on Turan's hypergraph problem, on novel applications of the lopsided Lovasz Local Lemma, on Sperner type and extremal poset problems. They will use combinatorial and probabilistic techniques in phylogenetics and in the theory of complex network.Scientific and engineering breakthroughs in many fields have spurred the development of new theory and algorithms for discrete structures. There is increasing demand to understand "optimal" extreme structures and "typical" random structures in discrete mathematics. This project will investigate basic combinatorial questions about structures and will look for various applications of discrete mathematics in computer science, biology, and engineering.