Lecture in summer term 2023.
Lecturer: Thore Posske
Course assistent: Ioannis Ioannidis
Schedule:
Lecture: Wed, 10:00 a.m.  11:30 a.m., Jungiusstr. 11, A208
Exercises: Wed, 11:45 a.m.  1:15 p.m., Jungiusstr. 11, blue saloon, B120
Only online lecture on: May 10, Conference
No lecture: May 17, Pentecost vacations
Last lecture: Wed, July 12.
Special lectures: June 28 and July 5: Guest lecture by Benedetta Flebus (Boston College, Mildred Dresselhaus guest professor), Nonhermitian physics and the SuSchriefferHeeger model
Topics, recommendations, and literature
Consent for video recording
Zoomlink
Exam/orals on Wed, August 2, 10 a.m.  2 p.m..
Voted on in second lecture
Oral, 30 minutes. Take care of the concrete appointments by writing me an email.
There will be a Questions and Answers session the Friday before the exam starting at 10:00 a.m.. Please send questions in advance.
1:
 Inspirations from topology

The Moebius strip

Foundations of topology

Metric spaces

2:
 Separation axioms

Partitions

3:
 Representations of topological spaces

Homotopies and contractible curves

Fundamental group  precursor calculations

4:
 Fundamental group  by drawing

Bogoliubov transforms

5:
 Symmetry reduction of Hamiltonians

The tenfold way

6:
 No exercises 
7:
 Conventional time reversal symmetry

8:
 The power of the matrix

9:
 MajoranaWavefunctions 
Adiabatic time evolution (see exercise sheet 10) 
10:
 Adiabatic time evolution

11:
 Linear representation up to a phase

Fun with braids

toggler: ↑ less ↑
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
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 ComputationFrom 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, noninteracting, topological phases
Ryu, Schnyder, Furusaki, Ludwig, classification of gapped, noninteracting, topological phases
Katos seminal paper about adiabatic time evolution