Interplay between Ergodic Theory, Additive Combinatorics and Ramsey Theory

这个项目旨在通过发展新的遍历理论方法来解决数论和组合学中的基本问题。该项目的预期结果包括在树的稠密子集中发现新的模式，获得强调加法和乘法独立性的严格的数论结果，在素数的稠密子集中发现无限模式，以及发展素数稠密模型理论的多维模拟。该项目将通过与从事遍历和数论工作的最好的国际和澳大利亚研究人员的深入合作，为澳大利亚的研究提供巨大的好处，并将用于教育新一代澳大利亚学生。

This project aims to address fundamental problems in Number Theory and Combinatorics by developing new innovative ergodic theoretic methods. Expected outcomes of the project include finding new patterns in dense subsets of trees, obtaining rigorous number-theoretic results emphasising the independence of addition and multiplication, finding infinite patterns in dense subsets of primes, and developing a multi-dimensional analogue of the dense model theory for primes. This project will provide significant benefits to Australian research via an intensive collaboration with best international and Australian researchers working in ergodic and number theory as well as will be used to educate a new generation of Australian students.