Quantum Groups and Categorification in Geometric Representation Theory

表象理论是对对称性的数学研究，在粒子物理、计算机科学和分子生物学等不同领域都有应用。这个项目的目的是使用一个新的量子群族来证明一个关于范畴和几何表示理论的猜想网络。该项目旨在回答几何表示理论中一个长期悬而未决的问题，该问题涉及李群理论背后的两个几何空间族。表示理论是澳大利亚数学的强项，该项目旨在这一动态领域的前沿进行紧迫的研究。

Representation theory, the mathematical study of symmetry, has applications in diverse areas such as particle physics, computer science, and molecular biology. This project aims to use a new family of quantum groups to prove a network of conjectures about categorical and geometric representation theory. The project aims to answer a long-standing open question in geometric representation theory concerning two families of geometric spaces underlying the theory of Lie groups. Representation theory is a strength of Australian mathematics, and this project aims to undertake pressing research at the forefront of this dynamic field.