Guo Chuang Thiang
(Beijing University)
May 4, 2022
Organized by Europe GNCG Seminar.

What is a Coarse Index, physically?

The coarse index of J. Roe beautifully expands index theory to noncompact manifolds.

It appears abstract at first glance, but I will explain how the coarse index counts:

(1) homological obstruction to quantum localization;

(2) connectedness of spectrum and anomalous currents;

(3) noncommutative families index and stability of Landau quantization.

These perspectives come directly from physics, and motivate NCG for Roe-type algebras.

Includes joint work with M. Ludewig and Y. Kubota.

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