Higher Representation Theory

表示论是一个数学领域，在数论和物理学等不同领域的数学研究中具有广泛的应用。高级（或范畴）表征理论的研究是一套现代工具，为表征理论现象提供了新的见解。这个项目的目的是研究分类的量子群，特别是，由图解代数提供的简化。该项目旨在进一步发展Khovanov-Lauda-Rouquier（KLR）代数的理论，为未来的研究提供重要的基础性成果。

Representation theory is a field of mathematics with applications across the breadth of mathematical study in fields as diverse as number theory and physics. The study of higher (or categorical) representation theory is a modern set of tools that provides new insights into representation theoretic phenomena. This project aims to study categorified quantum groups and, in particular, the categorifications provided by diagrammatic algebras. The project aims to further develop the theory of Khovanov-Lauda-Rouquier (KLR) algebras, providing important foundational results for future research to build upon.