Norbert Schappacher (Strasbourg), Marie-Françoise Roy (Rennes)
Paolo Aschieri (Alessandria and Torino)
Seiberg-Witten maps are a method to locally construct noncommutative gauge theories starting from commutative gauge theories. It originated in the context of gauge theories describing low energy effective actions in string theory. Geometrically, Seiberg-Witten maps provide a quantization of bundles with connections. We review their construction and apply it in the study of U(n)-vector bundles on two-dimensional tori, thus proving the existence of globally defined Seiberg-Witten maps. Time permitting we further show their compatibility with Morita equivalence (T-duality).