Intensive Course on Topology in Physics


Lecture at the CUI/SFB graduate school, January 2021
ZOOM-LINK, 10:00-12:00 a.m.
Schedule: Mo, Tue, Wed, Thu, Fr, Jan 11 2021 to Jan 15 2021, 10:00 - 12:00 a.m..


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All scripts in svg format (8x zoom needed)

Topology - Introduction
Contructing topological spaces
Topological classifications - Homotopy
What is gapped topological matter?
Classification of gapped topological matter (and fundamental symmetries)
The Kitaev Majorana chain
Z2 invariant of the Kitaev chain

Additional material

Fun with topology: Wind and Mr. Ug
Video lecture by John Milnor (Fields medalist, "Milnor spheres") about differential topology
Video lectures by Norman Wildberger about algebraic topology explained very intuitively
Video that the torus can be folded to a Moebius strip and corresponding Mathematica notebook
Notebook for numerically experimenting with the Kitaev chain's spectrum and topological phases

Recommended reading/references

Three lectures by Edward Witten on topology in condensed matter physics
Topology and physics - a historical essay, C. Nash
Topological Quantum Computation-From Basic Concepts to First Experiments, Stern, Ady and Lindner, Netanel H.
Preskill's lecture on Topological Quantum Computing
Seminal paper of Leinaas and Myrheim '77 describing anyons
Philosophical background on the "principle of indiscernibles"
Kitaev's periodic table of gapped, non-interacting, topological phases
Ryu, Schnyder, Furusaki, Ludwig, classification of gapped, non-interacting, topological phases
Katos seminal paper about adiabatic time evolution Time reversal symmetric Kitaev chains, Dumitrescu and Tewari 2013