Additive combinatorics, arithmetic algebraic geometry and finite fields

加法组合学、算术代数几何和有限域

• 批准号: DP170100786
• 负责人: Prof Igor Shparlinski
• 金额: $ 24.14万
• 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: 2017
• 资助国家: 澳大利亚
• 起止时间: 2017-06-30 至 2022-12-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP170100786
• 关键词: Additive; combinatorics; arithmetic; algebraic; geometry

This project aims to combine additive combinatorics and algebraic geometry and apply them to the theory of finite fields. Additive combinatorics and algebraic geometry are mostly developed over the complex numbers and other fields of characteristic zero. This project will bring the power of these different, discrete and continuous areas to finite fields, opening new perspectives for progress on several major problems, inaccessible by other methods. The project will advance and affect the development of number theory research in Australia and methodologies useful in mathematics and computer science, including cryptography.

该项目旨在将加法组合学和代数几何结合起来，并将其应用于有限域理论。加法组合学和代数几何主要是在复数和其他零特征域上发展起来的。该项目将把这些不同的、离散的和连续的领域的力量带入有限领域，为几个重大问题的进展开辟新的视角，这是其他方法无法实现的。该项目将推动并影响澳大利亚数论研究以及数学和计算机科学（包括密码学）有用方法的发展。