Topology in condensed matter systems

Zoom-link

Lecture in summer term 2026.
Lecturer: Thore Posske

Script & cheat sheet

Script and coursebook
Handwritten script
Cheat sheet (write me additionally suggested content for the cheat sheet)

Organization


Schedule:
Lecture: Wed, 10:00 a.m. - 11:30 a.m., Notkestr. 9/11
Exercises: Wed, 11:45 p.m. - 1:15 p.m., Notkestr. 9/11
No lecture: Start and end of May
Last lecture: Wed, June 15, 2026.
Topics, recommendations, and literature
Consent for video recording
Zoom-link

Questions and answers session

There is a questions and answers session on the last lecture date
Send questions until two days in advance.

Exam

Written exam, 90 minutes or oral exam, 20 minutes, depending on number of participants.
Registration at Stine additionally obligatory.
You are allowed to take a printout of the TICMS cheat sheet with you.

Content

toggler:  less 

Additional material

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

Topology In Condensed Matter: An Introduction - Miguel A N Araujo and Pedro Sacramento
Quantum Computation and Quantum Information - Michael Nielsen and Isaac Chuang
Altland's and Simons' book on Condensed Matter theory
Course on topology in condensed matter physics by Akhmerov et al.

Topology and physics - a historical essay, C. Nash
Topological Quantum Computation-From Basic Concepts to First Experiments, Stern, Ady and Lindner, Netanel H.
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