In this lecture note, we give a basic introduction to the rapidly developing concepts of generalized symmetries, from the perspectives of both high energy physics and condensed matter physics. In particular, we emphasize on the (invertible) higher-form and higher group symmetries. For the physical applications, we discuss the geometric engineering of QFTs in string theory and the symmetry-protected topological (SPT) phases in condensed matter physics.

中文翻译：

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关于广义对称性及其应用的讲义

在本讲义中，我们从高能物理和凝聚态物理的角度对快速发展的广义对称性概念进行了基本介绍。特别是，我们强调（可逆）更高形式和更高群对称性。对于物理应用，我们讨论了弦理论中 QFT 的几何工程和凝聚态物理中的对称保护拓扑 (SPT) 相。