Extremal and Probabilistic Combinatorics II

调查人员继续他们的工作，图形绘制和交叉号码，随机图形模型，重建，并在极值集和图论和离散几何的基本问题。特别是，他们将专注于图兰的超图问题，对新的应用不平衡的洛瓦兹局部引理，对斯珀纳型和极值偏序集问题。他们将在遗传学和复杂网络理论中使用组合和概率技术。许多领域的科学和工程突破促进了离散结构的新理论和算法的发展。在离散数学中，人们越来越需要理解“最优”极端结构和“典型”随机结构。本专题将探讨有关结构的基本组合问题，并寻找离散数学在计算机科学、生物学和工程学中的各种应用。

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.