Categorical geometry and perfect group schemes

本项目的目标是基于新发现的张量范畴构建新的几何理论，应用这些理论来解决表示论、代数和范畴论中的开放问题，并在有影响的仿射群格式理论和分类空间之间建立有益的新联系。几何理论将以一种普遍的方式发展，从物理学中推广经典代数几何和超几何，并专门研究无限多的新理论。这种普遍性为几何学在许多科学领域的长期应用提供了更为广泛的基础。其他好处包括加强澳大利亚的国际合作和科学能力。

The aims of this project are to construct novel geometric theories based on newly discovered tensor categories, to apply the theories to solve open problems in representation theory, algebra and category theory, and to establish profitable new connections between the influential theories of affine group schemes and classifying spaces. The geometric theories will be developed in a universal way, generalising both classical algebraic geometry and super geometry from physics, and specialising to infinitely many new theories. This universality ensures a significantly broader basis for long term applications of geometry in many areas of science. Other benefits include enhanced international collaboration and scientific capacity in Australia.