Measure theoretic frameworks for limsup sets

limsup 集的测量理论框架

• 批准号: DP200100994
• 负责人: Dr Mumtaz Hussain
• 金额: $ 28.44万
• 依托单位: La Trobe University
• 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 2024-12-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP200100994
• 关键词: Measure; theoretic; frameworks; limsup; sets

This project aims to develop new powerful measure theoretic techniques in mathematics that will be used in establishing some indispensable results in analytical number theory (Diophantine approximation) and dynamical systems. The plan is to construct new techniques and to use them in situations where existing techniques are not applicable. As a consequence of the proposed frameworks, not only we aim to resolve a few long-standing problems such as the Generalised Baker-Schmidt Problem (1970) but also envisage that the proposed frameworks will have far-reaching applications beyond the confines of Diophantine approximation and dynamical systems, for example, geometric measure theory, geometric probability and stochastic geometry etc.

该项目旨在开发数学中新的强大的测度理论技术，这些技术将用于建立解析数论（丢番图逼近）和动力系统中一些不可或缺的结果。该计划是建立新的技术，并在现有技术不适用的情况下使用它们。作为所提出的框架的结果，我们的目标不仅是解决一些长期存在的问题，如广义Baker-Schmidt问题（1970），但也设想所提出的框架将有深远的应用范围超出丢番图逼近和动力系统，例如，几何测度理论，几何概率和随机几何等。