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