Algebra

理解对称性，以及它是如何和为什么在自然界中产生的，在数学和物理学中都很重要。在我的工作中，最好的例子是在以仿射Kac-Moody李代数为公共桥梁的代数群和物理学之间的联系中找到的。测量对称性的数学对象称为群。李群是以19世纪末发现并首次研究这些天体的挪威数学家索菲斯·李的名字命名的，作为物理学中许多理论的基本对称性，李群自然而然地出现了。20世纪中叶见证了代数群的诞生，这种对象捕捉到了Lie群的精神，但更具普遍性。该研究项目的中心是了解代数群本身的性质，以及它们在数学和物理学的几个领域中的应用。

Understanding symmetry, and how and why it arises in nature, is important in both Mathematics and Physics. Within my work the best examples are to be found in the connections between Algebraic Groups and Physics that have the Affine Kac-Moody Lie algebras as a common bridge. The mathematical objects that measure symmetry are called Groups. Lie groups, named after the Norwegian mathematician Sophus Lie who discovered and first studied these objects late in the 19th century, arise naturally as the underlying symmetry of many theories in Physics. The mid 20th century saw the birth of Algebraic Groups, objects that capture the spirit of Lie groups yet are much more universal. The research project centres on understanding the very nature of algebraic groups themselves, and their applications to several areas of Mathematics, as well as Physics.