Local-Global Interactions in Combinatorics

数学科学的许多领域中的一个基本问题是，局部结构和全球结构如何相互作用。例如，关于大型复杂网络的本地结构，我们能说些什么呢？全球结构是如何受到我们在当地看到的约束的？这种类型的问题出现在许多领域，包括例如模型理论、几何群论、拓扑学、组合学、计算机科学、统计物理、生物学、概率论、网络科学和数据分析。实际的例子包括DNA测序，其中一个基因序列的片段需要组装成一个全局序列，以及大数据中的问题，其中全局结构太大，无法直接访问，其属性必须从“局部”信息中推断出来。这项研究的目的是解决关于图和网络中局部结构和全局结构之间的关系的基本问题。这将产生新的理论和新的结构理解，并导致对算法分析的新见解。

A fundamental question in many parts of the mathematical sciences is how local and global structure interact. For instance, what can we say about the local structures of a large, complicated network? How is global structure constrained by what we see locally? Problems of this type arise in many areas, including for example model theory, geometric group theory, topology, combinatorics, computer science, statistical physics, biology, probability, network science, and data analysis. Practical examples include DNA sequencing, where fragments of a genetic sequence need to be assembled to a global sequence, and problems in big data, where the global structure is too large to access directly and its properties must be inferred from 'local' information. The aim of this research is to address fundamental questions about the relationship between local and global structure in graphs and networks. This will generate new theory and new structural understanding, as well as leading to new insights into the analysis of algorithms.