Research Group:

## Non-commutative Geometry

Program:

0. Introduction.

1. Exterior and Clifford algebras, Spin groups, spinors.

2. Spin structures.

3. Dirac operator.

4. Some analytic properties. Spectral triple.

5. Other characteristic features: dimension (finite summability),

regularity (smoothness), finiteness & projectivity, reality,

first order, orientation, Poincare duality.

6. Statement of the ‘reconstruction theorem’ of A. Connes.

7. NCG Examples: noncommutative tori, spheres,

finite spectral triple for the Standard Model.