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In recent years there has been a series of striking developments in modern integral geometry which has, in particular, lead to the discovery of new relations to several branches of pure and applied mathematics. A number of examples were presented at this meeting, e.g. the work of Bernig, Solanes, and Fu on kinematic formulas on complex projective and complex hyperbolic spaces, that of Schneider and Vedel Jensen on tensor valuations and a series of results on convex body valued valuations by Abardia, Ludwig, Parapatits, and Wannerer.
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Semyon Alesker, Andreas Bernig, Franz E. Schuster, Integral Geometry and its Applications. Oberwolfach Rep. 10 (2013), no. 1, pp. 295–342