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The research program will be centered on noncommutative self-dual connections and their geometry. The starting point is the construction of vector bundles over noncommutative manifolds, instanton connections and their moduli spaces, and monopole connections. This for deformations associated with the actions of tori both real and algebraic. Several aspects of the construction and enumerations of noncommutative instantons will be considered (like iper Kaehler structures and desingularization) over such compact manifolds and on analogous ALE (noncompact) spaces. Equivariant cohomologies and localization methods will he studied also developping noncommutative versions of the Weil algebra and corresponding Weil homomorphism for a general Hopf algebra.
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