Deformation Quantization Methods for Algebras and categories with Applications to QuantumMechanics

Noncommutative geometry is often linked to deformation theory e.g. M. Kontsevich's work on star-products etc... The LUC group (M. Van Den Bergh, W. Lowen,...) have recently been active with deformation of categories, the UA-VUB groups used deformation techniques in studying Brauer groups of quantum groups or in the structure analysis of quantized algebras like generalized Weyl and Witten algebras. At different levels contact with Physics e.g. Statistical Physics, Quantum Mechanics could be observed. New recent developments seem to pont towards new applicability of the new theoretical methods. By cooperation with interested groups of researchers in Mathematical Physics, in particular the wellknown group at the University of Muenchen lead by Prof. J. Wess (with a.o. P. Schupp, B. Jurco, H.Steinacker, A. Boyka,...) and researchers of C. Isham's group at Imperial College (B. Hiley and others). The aim is to try to apply nonvommutative geometry and quantum groups to: quantumfield theory, gauge theory via gage algebras, new theory of deformed space-time. Perheps more concretely we have already partial results relating to Kochen-Specker theory and hidden variables, deformed Clifford algebras in braided categories with small braiding groups or low dimensional Hopf algebras.