Arithmetic and algebraic aspects of the dynamics of polynomial semigroups

多项式半群动力学的算术和代数方面

• 批准号: DP180100201
• 负责人: A/Prof Alina Ostafe
• 金额: $ 28.11万
• 依托单位: The University of New South Wales
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2018
• 资助国家: 澳大利亚
• 起止时间: 2018-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP180100201
• 关键词: Arithmetic; algebraic; aspects; dynamics; polynomial

This project aims to advance research in arithmetic dynamics, a rapidly developing field of mathematics that is rich in significant applications including cryptography. It will systematically study the semigroup action of several maps on an arithmetic space. The expected outcomes will extend existing concepts and theory, but also explore new mathematical phenomena related to number theory, graph theory and regular and chaotic arithmetic dynamics. There are likely applications in cryptography arising from the project and opportunities to build links between academia and national offices of information security.

该项目旨在推进算术动力学的研究，这是一个快速发展的数学领域，具有丰富的重要应用，包括密码学。系统地研究了算术空间上若干映射的半群作用。预期的成果将扩展现有的概念和理论，但也探索与数论，图论和规则和混沌算术动力学相关的新的数学现象。 该项目可能会产生密码学方面的应用，并有机会在学术界和国家信息安全办公室之间建立联系。