Interplay between Ergodic Theory, Additive Combinatorics and Ramsey Theory

该项目旨在通过开发新的创新遍历理论方法来解决数论和组合学中的基本问题。该项目的预期成果包括在密集的树子集中找到新的模式，获得严格的数论结果，强调加法和乘法的独立性，在密集的素数子集中找到无限的模式，以及开发一个多维的类似于素数的密集模型理论。该项目将通过与在遍历和数论领域工作的最佳国际和澳大利亚研究人员的密切合作，为澳大利亚的研究提供重大利益，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.