New Applications of Additive Combinatorics in Number Theory and Graph Theory

该项目旨在显著推进加性组合学、数论和图论之间的相互作用。该项目将使用和推进加性组合学的方法和结果，并为Cayley图上的连通性、随机游走、着色和支配集等基本问题提供新的应用。这个项目的意义在于，它的目标是推进加性组合学的现有结果和方法，并找到它们的新应用，这些应用对关键通信网络架构基础上的Cayley图的重要问题具有持久的影响。在这些问题上取得进展和发展相关的加性组合方法将是主要的成果。

The project aims to advance significantly the interplay between additive combinatorics, number theory and graph theory. The project will use and advance methods and results of additive combinatorics and give new applications to such fundamental problems on Cayley graphs as connectivity, random walks, colouring and dominating sets. The significance of the project is ensured by its goal of advancing existing results and methods of additive combinatorics and also in finding their new applications that have long-lasting impact on paramount problems for Cayley graphs that underlie the architecture of crucial communication networks. Achieving progress on these problems and developing relevant methods of additive combinatorics will be the main outcomes.