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CR geometry is the geometry of real hypersurfaces in C^n preserved by loca ambient biholomorphisms. The problem of understanding CR geometries embedded as submanifolds in higher dimensional CR manifolds arises in the study of proper holomorphic mappings and of singularities of analytic varieties. It has also been studied intensively in connection with rigidity questions. Despite considerable earlier work the local theory has not been fully understood.

We develop from scratch a CR invariant local theory based on CR tractor calculus (i.e. the associated bundle). This produces the tools for constructing local invariants and invariant operators in a way parallel to the classical Gauss-Codazzi-Ricci calculus for Riemannian submanifolds. It also enables a practical and conceptual approach to a Bonnet Theorem and potentially the rigidity questions.he problem of understanding CR geometries embedded as submanifolds in higher dimensional CR manifolds arises in higher dimensional complex analysis, including the study of singularities of analytic varieties. It has also been studied intensively in connection with rigidity questions. Despite considerable earlier work the local theory has not been fully understood.

Coffee and pastries served before the talk ~12:45