Metrics of special holonomy are of central interest in both Riemannian and complex algebraic geometry. We focus on an important classification problem of a particular type of special holonomy manifolds, namely compact quaternion-Kähler with positive scalar curvature (Salamon-LeBrun conjecture). In the language of algebraic geometry this corresponds to the classification of Fano contact manifolds. By bringing together leading experts in both fields this workshop pursued a two-fold goal: First, to revise old and to develop new strategies for proving the most central conjecture in the field of quaternionic Kähler geometry. Second, to introduce young researchers at PhD/PostDoc level to this interdisciplinary circle of ideas.
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Anna Fino, Uwe Semmelmann, Jaroslaw A. Wisniewski, Frederik Witt, Mini-Workshop: Quaternion Kähler Structures in Riemannian and Algebraic Geometry. Oberwolfach Rep. 10 (2013), no. 4, pp. 3115–3145DOI 10.4171/OWR/2013/53