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Exact (fractional) quantization and large-scale algebraic topology

组织者

白岸斯 , 陈群皓 , 孔良 , 王亦龙 , 张智浩 , 郑浩

演讲者

Guo Chuan Thiang

时间

2025年02月18日 09:45 至 11:30

地点

A3-2-301

线上

Zoom 468 248 1222 (BIMSA)

摘要

The quantum Hall effects are dramatic manifestations of exact (fractional) quantization in macroscopic laboratory samples. Although this type of phenomenon is commonly said to be "topological", it surely is "non-topological" due to its insensitivity to microscopic details, such as holes in samples. I will explain how to understand exact quantization in terms of a macroscopic index theory for Hamiltonians on non-compact manifolds, where the topological category is enhanced to incorporate coarse-grained metric data. As an example, we will prove that Landau levels possess exactly rational trace formulae, indicating its potential for hosting ground states with fractional Hall conductances and anyonic excitations.