Extremal and Probabilistic Combinatorics II

研究者们继续研究图的绘制和交叉数、随机图模型、系统发育重建，以及极值集、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，不平衡Lovasz局部引理的新应用，Sperner型和极值偏置集问题。他们将在系统发育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刺激了离散结构的新理论和新算法的发展。在离散数学中，对“最优”极端结构和“典型”随机结构的理解需求日益增加。这个项目将研究关于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.