Lecturer:

Course Type:

PhD Course

Academic Year:

2013-2014

Period:

October-November

Duration:

20 h

Description:

- 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.

- Index Theory.
- The Index of Fredholm operators: Properties: additivity and homotopy invariance. Explicit computations for the case of S1: the winding number.

Research Group:

Location:

A-136