New frontiers in the theory of noncommutative surfaces

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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.