Tuesday, February 22, 2022 - 10:00 in V2-213
Gap Labelling: What is it and why is it useful?
A talk in the Other series by
David Damanik
| Abstract: |
We give an introduction to the gap labelling theorem, due to Bellissard et al. Gap labelling
involves the identification of a set of natural labels of spectral gaps of dynamically defined
operators that only depends on the base dynamics and is uniform in the sampling function. In the
special case of one-dimensional Schrödinger operators we present Johnson’s approach to this result,
which is based on the Schwartzman homomorphism. If time permits, some recent applications
of gap labelling, both in terms of the presence and the absence of spectral gaps, will be discussed.
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