# 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 Z
_{2 }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