Noncommutative Geometry and Topology in Prague

Differentiable positive maps, vector fields, divergences, exponentials, parallel transport, quantum mechanics and state spaces

The talk discusses a mixture of topics in noncommutative differential geometry which are all related by the idea of connection on bimodules. We see how exponentiation of invariant vector fields on the integers is almost, but not quite, the same as diffusion. We consider the exponential map on quantum SU_2. We see how the universal calculus on matrices is related to the usual calculus on complex projective space. We look at noncommutative fluid mechanics (well a little bit)… And we ask whether there really is a probabilistic interpretation of the Klein Gordon equation.

Joint work with Shahn Majid and Ghaliah Alhamzi