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Elliptic fibrations play a central role in the geometry of complex surfaces, and there is a comprehensive array of theory and examples. They arise also as a tool in many applications, such as the construction of rational points in arithmetic, metrics in differential geometry and certain string dualities in physics. In higher dimensional geometry, the foundational results of the past 30 years have not yet developed into a practical collection of everyday tools, as they have in the surface case. Nevertheless, the applications already work in higher dimensions – a glance at the literature shows the extent to which practical calculations in physics alone now far outpace the existing theory. This workshop brings together geometers, physicists and others to compare applications of elliptic fibrations and the state of the general theory.
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Gavin D. Brown, Anda Degeratu, Katrin Wendland, Mini-Workshop: Higher Dimensional Elliptic Fibrations. Oberwolfach Rep. 7 (2010), no. 4, pp. 2651–2680