The Mathematics of Topological Insulators in Naples
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02/02/2015 15.30-17.30 dr. G.Panati
An introduction to Chern insulators
Topological phases of matter, Kitaev's periodic table
Bloch-Floquet theory, Bloch bundles and their Chern classes
Is the Chern number observable?
03/02/2015 14.30-16.00 dr. G.Panati
An introduction to Z_2 topological insulators
Periodic Schrödinger operators with TR-symmetry
Existence of TR-symmetric Bloch frames?
03/02/2015 16.30-18.00 Prof. G.M.Graf
Quantum Hall effect (QHE): What is it?
Views of the Quantum Hall effect: As a pump, as a bulk effect, and as an edge effect.
04/02/2015 14.30-16.30 Prof. G.M.Graf
Mathematical details: Spectral flow and Fredholm indices; linear response and the Kubo formula;
Equivalences between views
05/02/2015 14.30-16.30 Prof. G.M.Graf
The periodic case: fiber bundles, the Great Wall, and butterflies
Topological insulators: What are they?
The Pfaffian indices and the Rueda
Bulk and Edge equivalence
Details on the 3d case
M.Z. Hasan, C.L. Kane, Topological Insulators, Reviews of Modern Physics, Vol 82, 2010.
S.Q. Shen, Topological Insulators, Springer 2012.
The meeting will be broadcast on our channel