Geometry and representations of classical and quantum Lie supergroups

超对称性的物理概念是一个统一的原理，它确保量子物理中的玻色子和费米子粒子遵守相同的基本定律。自20世纪80年代以来，它一直渗透到数学研究的前沿，导致在不同领域创造了一些最深层次的理论。超对称的数学基础在于李超群理论。这个项目解决了李超群及其量子类似物的几何和表示的主要悬而未决的问题。结果对于寻求一个关于自然界中所有四种相互作用的一致的量子理论将是重要的。

The physical notion of supersymmetry is a unifying principle which ensures that bosonic and fermionic particles in quantum physics obey the same fundamental laws. It has permeated the forefront of mathematical research since 1980s, leading to the creation of some of the deepest theories in diverse areas. The mathematical foundation of supersymmetry lies in the theory of Lie supergroups. This project addresses major outstanding problems in the geometry and representations of Lie supergroups and their quantum analogues. Results will be important to the quest for a consistent quantum theory of all the four interactions in nature.