New frontiers in the theory of noncommutative surfaces

在90年代，阿廷推出了他的学校的非交换代数几何，其中新颖的几何方法， 被用来深刻地加深我们对非交换代数这一经典课题的理解。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。该项目期望开发新的方法，包括层理论，Mori的最小模型程序， 模栈，特别是研究，阿廷的分类问题的非交换表面。预计 成果包括对非交换代数的更丰富的几何理解。这个项目应该有助于 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.