Research Group:

## Basics of Noncommutative Geometry

- Noncommutative Topology.
- Motivation. The dictionary.

- Noncommutative Geometry.
- Spectral Triples: The data set. The compact resolvent condition. Boundedness of the commutators. Examples of spectral triples: the circle S1; the noncommutative torus.
- Spectral Dimension and the zeta function: Definition. The trace property. Computations for the examples. Gauss-Bonnet for the noncommutative two torus.