Seminar on Theoretical Physics: Topology: From Mathematics to Physics
Prof. Dr. Carsten Timm
carsten.timm@tu-dresden.de
Room A 101, Zellerscher Weg 17
Office hours: Tuesday 08:00-10:00 and by appointment (preferred)
This page contains information on the Seminar on Theoretical Physics: Topology: From Mathematics to Physics. The seminar will start with preliminary discussions on Wednesday, October 16, 3rd teaching period (11:10) in room BZW/A120. The first talk will take place on November 6.
In the last years, topological concepts have played an increasingly important role in physics, in particular in the physics of condensed matter. This is reflected by a collaborative research center and a cluster of excellence at TU Dresden, which are dealing with this field of research. In this seminar, both the mathematical basis and applications in (solid-state) physics will be discussed in talks given by the participants. The focus will depend on the participants' interests. It is possible to combine aspects of methodology and corresponding applications in a single talk. Presentations can be given in German or English. Topics will be assigned in the first week.
Selection of possible topics:
- Mathematical foundations
- Basic concepts of topology
- Homotopy theory
- K theory: introduction
- Atiyah-Singer index theorem
- Bott periodicity
- Theory of knots
- Applications in solid-state physics: real space
- Topological defects: vortices, hedgehogs, skyrmions, etc. (with homotopy?)
- Kosterlitz-Thouless theory
- "Toric code" model
- Spin liquids: Kitaev model on the honeycomb lattice
- Applications in solid-state physics: reciprocal space
- Berry phase
- Classification of topological insulators and superconductors: "ten-fold way"
- Topological insulators with Z2 invariant
- Crystalline topological insulators
- Classification of Fermi manifolds
- Weyl semimetals and chiral anomaly
- Skyrmions and topological Hall effect
- Non-centrosymmetric superconductors
- Topological superconductors with Bogoliubov Fermi surfaces