Mathematics

The  lectures are planned to be a gentle introduction to the theoryof Hilbert C*-modules, with  an emphasis on their dynamical interpretationand universal C*-algebras they model.Amongst the topics we plan to cover are:i) Basic facts on Hilbert modules - Examples. Interpretation of Hilbert C*-modules as non-commutative vector bundles. Adjointable maps.ii) C*-correspondences and internal tensor product of Hilbert modules. Interpretation of C*-correspondences as dynamical objects - noncommutative topological graphs. Induced representations.iii) Hilbert bimodules and Morita equivalence.iv) C*-algebras associated to actions of C*-correspondences - Fell bundles, product systems, Cuntz-Pimsner algebras.Time permitting we will also mention how to interpret K-theoryand KK-theory from the Hilbert module perspective.