Multi-dimensionally consistent integrable systems in geometry and algebra

该项目旨在以创新的方式解决非线性数学中一个长期存在的开放问题，即确定可积系统的代数和几何起源。它有望对可积系统理论做出根本性的贡献。后者提供了独特的访问非线性现象的分析处理不仅在物理学，而且在数学领域的显着不同。预期成果包括离散环境中的扩展、统一和新颖的关键数学概念及其在代数和几何背景下的应用。由于参与者的选择，预计澳大利亚将受益于加强与德国的研究合作。

This project aims to address in an innovative manner a long-standing open problem in nonlinear mathematics, namely the determination of the algebraic and geometric origin of integrable systems. It is expected to make a fundamental contribution towards integrable systems theory. The latter provides unique access to the analytic treatment of nonlinear phenomena not only in physics but also a remarkably diverse range of areas in mathematics. Expected outcomes include extended, unified and novel key mathematical concepts in a discrete setting and their applications in algebraic and geometric contexts. Due to the choice of participants, it is anticipated that Australia will benefit from strengthened research collaborations with Germany.