New frontiers in the theory of noncommutative surfaces

在90年代，Artin创立了他的非对易代数几何学派，其中新的几何方法 用来深刻加深我们对非对易代数这门经典学科的理解。这 该项目旨在通过在非对易理论中建立几个新的前沿来推进这一理论 表面。这个项目期望开发新的方法，涉及Sheaf理论，Mori的最小模型程序和 为了特别研究非对易曲面的Artin分类问题，模堆叠。预期 结果包括对非对易代数有了更丰富的几何理解。这个项目应该会有帮助 确保澳大利亚在代数和代数几何的重要发展中发挥主导作用。

In the 90s, Artin launched his school of noncommutative algebraic geometry, where novel geometric methods were used to profoundly deepen our understanding of the classical subject of noncommutative algebra. This project aims to advance this theory by establishing several new frontiers in the theory of noncommutative surfaces. This project expects to develop new methods involving sheaf theory, Mori's minimal model program and moduli stacks, to study in particular, Artin's classification problem for noncommutative surfaces. Expected outcomes include a much richer geometric understanding of noncommutative algebra. This project should help ensure Australia plays a leading role in important developments in both algebra and algebraic geometry.