Additive combinatorics, arithmetic algebraic geometry and finite fields

本项目旨在将加性组合学与代数几何相结合，并将其应用于有限域理论。加性组合学和代数几何主要是在复数和特征为零的其他领域上发展起来的。这个项目将把这些不同的、离散的和连续的领域的力量带到有限的领域，为其他方法无法实现的几个主要问题的进展开辟新的视角。该项目将推动和影响澳大利亚数论研究的发展，以及对数学和计算机科学（包括密码学）有用的方法。

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.