Mathematics

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.

If time permits:
8. Symmetries: actions and coactions of Hopf algebras