Additive combinatorics of infinite sets via ergodic theoretic approach

通过遍历理论方法的无限集的加性组合

• 批准号: DP210100162
• 负责人: A/Prof Alexander Fish
• 金额: $ 23.88万
• 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: 2021
• 资助国家: 澳大利亚
• 起止时间: 2021-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP210100162
• 关键词: Additive; combinatorics; infinite; sets; via

The proposed project will utilise innovative ergodic theoretic approaches to enable us to address important questions in Additive Combinatorics (Number Theory) and Fractal Geometry. In particular, we will resolve long-standing inverse additive problems for infinite sets, discover sum-product phenomena in Number Theory, and find a plethora of finite configurations in fractal sets. We will also extend the structure theory of one of the most popular mathematical models of quasi-crystals to a more extensive class of groups. This project will make significant contributions to Additive Combinatorics and Ergodic Theory and will bring the Australian research in these fields to ever greater heights.

该项目将利用创新的遍历理论方法，使我们能够解决加法组合学（数论）和分形几何中的重要问题。特别是，我们将解决长期存在的无穷集合的逆加法问题，发现数论中的和积现象，并在分形集合中找到大量的有限配置。我们还将把准晶体最流行的数学模型之一的结构理论扩展到更广泛的一类群。该项目将对加法组合学和遍历理论做出重大贡献，并将使澳大利亚在这些领域的研究达到更高的水平。