Nuclei with closed-shell have spherical symmetries.

闭壳核具有球对称性。

They are symmetries of the sphere.

这就是球的对称性。

But studying such symmetries required a whole new language.

但研究这类对称需要全新的语言。

Symmetries and variations are also interlaced on the upper floors.

对称性和变化也交错楼上。

Subfactor theory is a natural framework to study quantum symmetries.

讲座摘要：子因子提供了一个研究量子对称性的理论框架。