Higher Representation Theory

表征理论是数学的一个领域，在数论和物理学等不同的数学研究领域都有广泛的应用。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。本项目旨在研究有范畴的量子群，特别是由图代数提供的范畴。该项目旨在进一步发展Khovanov-Lauda-Rouquier （KLR）代数理论，为未来的研究提供重要的基础成果。

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.