Shuffle algebras and vertex models

Shuffle代数是一种重要的新的数学结构，它为解决数学物理、代数几何和组合数学等众多数学分支中的未决问题提供了新的方法和技术。这个项目提出使用洗牌代数和可积格模型之间的联系来找到关键开放问题的解决方案。预期的成果包括：（i）一个新的框架的洗牌代数技术，以解决具有挑战性的研究问题，在数学物理和统计力学，（ii）实际和计算上可行的结构洗牌代数使用顶点模型，（iii）解决未解决的光谱问题的开放量子系统。

Shuffle algebras are important new mathematical structures that offer a new approaches and techniques to solve outstanding open problems in a variety of branches of mathematics, including mathematical physics, algebraic geometry and combinatorics. This project proposes to find solutions to key open problems using connections between shuffle algebras and integrable lattice models. The expected outcomes include (i) a new framework of shuffle algebra techniques to solve challenging research problems in mathematical physics and statistical mechanics, (ii) practical and computationally feasible constructions of shuffle algebras using vertex models, (iii) solutions to unresolved spectral problems of open quantum systems.