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BIMSA TQFT and Higher Symmetries Seminar
Exact (fractional) quantization and large-scale algebraic topology
Exact (fractional) quantization and large-scale algebraic topology
Organizers
Speaker
Guo Chuan Thiang
Time
Tuesday, February 18, 2025 9:45 AM - 11:30 AM
Venue
A3-2-301
Online
Zoom 468 248 1222
(BIMSA)
Abstract
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.