New techniques for exponential sums over low degree polynomials

本项目旨在获得低次多项式上Weyl和的新的定量估计。这样的估计是数论几个领域的基础。通过结合不同数学领域的技术，包括代数几何、解析数论、数字几何和调和分析，该项目将在一个多世纪以来首次在估计低次多项式的Weyl和方面取得进展。预期成果包括加深对Weyl sum的理解和加强国际合作。这样的进展将使澳大利亚处于数论这一重要分支的前沿。

This project aims to obtain new quantitative estimates for Weyl sums over low degree polynomials. Such estimates are fundamental to several areas of number theory. By interfacing techniques from diverse areas of mathematics, including algebraic geometry, analytic number theory, the geometry of numbers and harmonic analysis, this project will provide the first progress on estimating Weyl sums over low degree polynomials in over a century. The expected outcomes include a deeper understanding of Weyl sums and enhanced international collaborations. Such progress will place Australia at the forefront of this important branch of number theory.