New directions in Hecke algebras

这个项目的目标是在表示理论中取得根本性的进展，这是一个强大的数学分支，专注于抽象的数学结构，并以具体和有用的方式“表示”它们。特别地，我们的目标是证明George Lusztig关于Hecke代数的表示理论的一系列长期和有影响力的猜想，Hecke代数是现代代数中普遍存在的对象。我们的工作将带来新的发现，从根本上加深对Kazhdan-Lusztig理论的理解，并将推动未来的研究。好处包括加强国际合作和提高纯数学的能力，特别是在表示理论的前沿领域。

To goal of this project is to make fundamental advances in representation theory, a powerful branch of mathematics focused on taking abstract mathematical structures and ``representing'' them in a concrete and useful way. In particular we aim to prove a series of long standing and influential conjectures by George Lusztig concerning the representation theory of Hecke algebras, objects which are ubiquitous in modern algebra. Our work will lead to new discoveries, a fundamentally deeper understanding of Kazhdan-Lusztig theory, and will drive future research. Benefits include enhanced international collaboration and increasing capacity in pure mathematics, especially in the cutting-edge area of representation theory.