Abstract
A survey on recent developments in (algebraic) integral geometry is given. The main focus lies on algebraic structures on the space of translation invariant valuations and applications in integral geometry.
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Acknowledgements
I was happy to profit from many discussions with and talks by Semyon Alesker and Joseph Fu on algebraic integral geometry. The present text is strongly influenced by their ideas and I am grateful to them. The terms Algebraic integral geometryand Fundamental theorem of algebraic integral geometrywere invented by Fu. I also thank Gautier Berck, Franz Schuster and Christoph Thäle for numerous useful remarks on this text.
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Bernig, A. (2012). Algebraic Integral Geometry. In: Bär, C., Lohkamp, J., Schwarz, M. (eds) Global Differential Geometry. Springer Proceedings in Mathematics, vol 17. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22842-1_5
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