New dualities in modular representation theory

本课题旨在介绍一般线性群的模表示理论中新的几何技术，解决正交群和辛群的模表示的基本问题。表征理论，对称的数学研究，在从物理学到计算机科学的许多领域都有应用。模的设定，其中场的特征是正的，是这个主题最深刻的猜想的来源。最近的突破为模表示理论中一些以前无法触及的问题提供了方法。该项目将促进该领域前沿的研究，并有助于保持澳大利亚的国际地位。它将培养澳大利亚的研究生，他们将能够将他们的研究技能应用于工业，并加强澳大利亚与充满活力的国际社会的联系。

This project aims to introduce new geometric techniques in the modular representation theory of the general linear group, and resolve fundamental questions about modular representations of orthogonal and symplectic groups. Representation theory, the mathematical study of symmetry, has applications in many areas ranging from physics to computer science. The modular setting, where the characteristic of the field is positive, is a source of the deepest conjectures in this subject. Recent breakthroughs have provided approaches to some problems in modular representation theory that were previously inaccessible. This project will promote research at the forefront of the field, and help maintain Australia's international standing. It will train Australian postgraduates, who will be able to apply their research skills in industry, and strengthen the country's ties to a vibrant international community.