Discovery Projects - Grant ID: DP210100951

有限维可积系统与微分几何。科学(物理、工程)和现实世界(自然、经济)中许多过程的数学模型都由复杂的微分方程组支配。一类重要的、杰出的此类模型是由可积系统描述的，可积系统可以提供一个全面的定性图像，在许多情况下，还可以提供一个完整的解决方案。利用最近发展起来的强大的可积系统和微分几何方法，这个项目将专注于这两个学科中一系列重要的、相互关联的理论问题。预期结果将提供新的、深刻的、在数学上和物理上意义重大的结果，这些结果将导致在一系列领域的应用和发展。

Finite dimensional integrable systems and differential geometry. Mathematical models of many processes in science (physics, engineering) and in the real world (nature, economics) are governed by complicated systems of differential equations. An important, distinguished class of such models is described by integrable systems, the systems for which one can provide a comprehensive qualitative picture, and in many cases, a complete solution. Using recently developed, powerful methods of integrable systems and differential geometry, this project will focus on a range of important, interconnected theoretical problems in both disciplines. The expected outcomes will provide new, deep, mathematically and physically significant results which will lead to applications and developments across a range of fields.