Interplay between Ergodic Theory, Additive Combinatorics and Ramsey Theory

遍历理论、加法组合学和拉姆齐理论之间的相互作用

• 批准号: DP240100472
• 负责人: A/Prof Alexander Fish
• 金额: $ 32.87万
• 依托单位: The University of Sydney
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2024
• 资助国家: 澳大利亚
• 起止时间: 2024-01-01 至 2026-12-31
• 项目状态: 未结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP240100472
• 关键词: Interplay; between; Ergodic; Theory; Additive

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.

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树的稠密子集中找到新的模式，获得强调加法和乘法独立性的严格数论结果，在素数的稠密子集中找到无限模式，以及开发稠密模型理论的多维模拟对于素数。该项目将通过与国际和澳大利亚从事遍历和数论研究的最佳研究人员的密切合作，为澳大利亚的研究带来巨大的好处，并将用于教育新一代的澳大利亚学生。