Cherednik Algebras at Infinity

许多人喜欢对称给设计带来的形式上的优雅。不太为人所知的是19世纪世纪的数学发现，对称性形成了几何学的框架。后来，世纪的物理学家发现，这些相同的想法是我们理解宇宙的核心。数学中有一个特殊的分支，称为表示论，它研究数学和其他科学领域（包括生物学，化学和物理学）中的对象和现象所揭示（或有时隐藏）的对称性。该分支是项目的区域。该项目的目的是研究特定的对象，称为Cherednik代数或双仿射Hecke代数。它们出现在大约20年前，是融合了现代理论物理学的分支共形场论和更传统的数学分支特殊函数理论的结果。从那时起，Cherednik代数被发现发挥重大作用，在其他几个分支的数学。我们的目标是推进这些代数的理论，并找到更多的数学和理论物理之间的联系。

Many people delight in the formal elegance the symmetry can bring to a design. Less well known is the 19th century mathematical discovery that symmetry forms the framework for Geometry. Later, 20th century physicists discovered that these same ideas lie at the heart of our understanding of the Universe. There is a special branch of Mathematics, called Representation Theory, which studies symmetries revealed (or sometimes concealed) by objects and phenomena in Mathematics and other fields of Science including Biology, Chemistry and Physics. That branch is the area of the project. The aim of the project is to study particular objects, called Cherednik algebras or double affine Hecke algebras. They appeared about 20 years ago as a result of blending ideas from the branch of modern Theoretical Physics called Conformal Field Theory, and from a more traditional branch of Mathematics, called the Theory of Special Functions. Since then the Cherednik algebras were found to play major roles in several other branches of Mathematics. We aim to advance the theory of these algebras, and to find more links between Mathematics and Theoretical Physics.