``Intro to quantum algebra"

January 31 | Wade Bloomquist (UCSB)

**Past:**

January 17 | Chao-Ming Jian (Microsoft)

**Folding approach to topological orders enriched by mirror symmetry**

In 2+1D, the symmetry-enriched topological orders (SET) with local unitary symmetry can be systematically studied using the framework of G-crossed braided tensor category. In contrast, the SETs with mirror reflection symmetry require different techniques due to the non-local and orientation-reversing nature of the symmetry action. In this talk, I will introduce a folding approach that maps the SET with mirror symmetry to a bilayer system local unitary Z2 symmetry. The essential information of the mirror symmetry fractionalization in the original system will be mapped to the topological data of gapped boundaries in the bilayer system which can be then systematically studied using the anyon condensation theory. Using this approach, I will discuss the physical constraints on data that describe mirror SETs as well as the mirror symmetry quantum anomaly.